supplement  to  the 

Annals  of  the  American  Academy  of  Political  and  Social  Science, 

march,  1 89 1. 


HISTORY, THEORY,  AND  TECHNIQUE 


OF 


STATISTICS 


BY 


U*JU 


AUGUST  MEITZEN,  Ph.D., 

PROFESSOR  AT  THK  UNIVERSITY  OF   BERLIN. 


TRANSLATED,    WITH     AN      INTRODUCTION, 


BY 
ROLAND  P.  FALKNER,  Ph.D., 

m 

INSTRUCTOR  OF  STATISTICS,  UNIVERSITY  OF  PENNSYLVANIA. 


PART    FIRST: 
HISTORY  OF  STATISTICS. 


PHILADELPHIA: 

AMERICAN  ACADEMY  OF  POLITICAL  AND  SOCIAL  SCIENCE. 

189I. 


*$ 


INTRODUCTION    BY    THE    TRANSLATOR. 


In  presenting  to  the  English  public  a  work  like  the  present  a  word 
of  explanation  seems  in  order.  Professor  Meitzen's  work,  "Geschichte, 
Theorie,  und  Technik  der  Statistik,"  represents  the  most  complete 
statement  of  theoretical  statistics,  in  the  smallest  compass,  in  the 
German  language.  Its  translation  therefore  has  appeared  desirable  as 
well  on  account  of  its  form  as  its  matter. 

In  regard  to  form,  the  work  covers  systematically  the  whole  field  of 
statistical  theory,  and  thus  furnishes  the  student  an  insight  into  the 
relation  of  the  parts  not  to  be  gained  by  the  consideration  of  special 
problems.  In  this  respect  the  work  represents  a  familiar  habit  of  the 
German  mind  which  has  some  signal  advantages.  We  are  apt  in  Eng- 
land and  America  to  devote  our  study  to  special  problems,  and  whole 
fields  of  research,  long  since  systematized  in  Continental  Europe,  and 
there  known,  inaptly  perhaps,  as  sciences,  must  be  studied  by  the 
English  student  from  treatises  on  special  subjects,  and  he  must  in  his 
own  thought  establish  the  connecting-links  which  bring  about  the 
harmony  of  the  whole.  If  it  be  necessary  to  adduce  instances  of  this 
fact  let  us  consider  for  a  moment  the  whole  subject  of  public  finance. 
An  exhaustive  treatment  of  the  subject  in  English  cannot  be  named, 
whereas  the  student  of  the  subject  at  once  recalls  the  names  of  Ger- 
man, French,  and  Italian  writers  who  have  devoted  systematic  treat- 
ises to  it.  The  same  is  true  of  other  topics,  but  notably  so  of  that 
which  we  are  now  considering,  statistics.  It  may  be*A*mbted  whether 
the  conception  of  statistics  as  a  connected  organic  science  is  familiar 
even  to  those  whose  achievements  in  this  field  have  been  most  hon- 
orable. Certainly  no  exhaustive  treatise  on  the  subject  exists  in  our 
language  despite  the  valued  contributions  made  by  English  science  to 
the  subject.  Hence  the  translation  of  the  present  work  has  been  pre- 
pared partly  with  a  view  to  the  opportunity  which  it  afforded  for  the 
comparison  of  German  methods  of  thought  with  our  own.  No  attempt 
will  be  made  here  to  weigh  the  relative  merits  of  each.  Only  in 
passing  it  may  be  observed  that  if  the  German  plan  tends  to  a  super- 
ficial treatment  of  certain  subjects  in  the  endeavor  to  preserve  the 
symmetry  of  the  system,  our  own  more  special  investigation  tends  to 

(3) 


iOO 


4  Annals  of  the  American  Academy. 

deprive  us  of  that  insight  into  the  general  relations  of  things  which 
illuminates  and  corrects  our  conception  of  special  problems. 

Now  as  respects  the  contents  of  the  work,  it  may  be  remarked  that 
the  general  interest  in  statistical  results,  and  the  increasing  use  of 
statistical  figures  in  all  kinds  of  scientific  and  popular  discussion,  are 
in  marked  contrast  to  the  paucity  of  our  scientific  literature  on  the 
subject  of  statistics  itself,  which  furnishes  an  additional  motive  for 
the  present  translation.  In  England  we  have  the  valuable  works  of 
Farr  and  Newsholme,  and  the  Journal  of  the  Statistical  Society,  in 
the  United  States  the  suggestive  monograph  of  Prof.  R.  M.  Smith 
on  "  Statistics  and  Economics,"  and  the  publications  of  the  American 
Statistical  Association,  besides  certain  highly-prized  official  docu- 
ments, and  special  studies  from  which  the  student  of  statistics  may 
gather  invaluable  suggestions  as  to  the  statistical  method  and  a 
keen  insight  which  prevents  his  erring  in  the  use  of  it.  Nevertheless 
a  complete  formulation  of  the  method  and  its  processes,  reinforcing 
that  statistical  instinct  which  is  essential  to  all  true  work,  is  lacking  in 
our  literature.  It  is  in  part  with  the  view  of  supplying  this  deficiency 
that  the  translation  has  been  undertaken.  Prof.  Meitzen's  clear  and 
logical  discussion  of  the  processes  of  statistical  argument  must,  we 
believe,  be  helpful  to  all  who  are  confronted  by  such  arguments  and 
who  feel  the  necessity  of  testing  their  reliability.  If  not  the  purpose, 
it  is  at  least  the  result  of  the  work  that  it  furnishes  the  tests  whereby  we 
can  readily  ascertain  whether  a  statistical  argument  can  hold  water. 
The  Translator  takes  pleasure  in  acknowledging  that  in  his  own  work 
he  owes  more  to  the  inspiration  of  the  present  work  than  to  any  other 
treatment  of  the  subject  of  statistics.  To  make  the  same  opportuni- 
ties accessible  to  the  English  public  as  far  as  may  be  possible  is  the 
aim  of  the  translation.  It  is  our  sincere  conviction  that  the  study  of 
statistical  methods  is  not  a  merely  theoretical  but  an  eminently  prac- 
tical one,  a  necessary  corrective  of  that  false  use  of  statistical  results 
which  is  everywhere  so  abundant,  and  which,  as  we  glean  from  the 
author's  preface,  is  as  much  an  evil  in  Germany  as  it  is  among  us. 
It  is  hoped  that  the  present  work  may  accomplish  something  toward 
spreading  more  accurate  conceptions  of  the  possibilities  and  the 
limits  of  statistical  argument. 
.  Statistics,  according  to  Prof.  Meitzen,  is  a  method  of  scientific  inves- 
tigation by  means  of  enumeration  of  objects  and  the  numerical  com- 
parison of  the  results  of  such  enumeration.  Hence  they  may  be 
applied  to  any  field  whatever  of  human  knowledge  if  the  necessary 
conditions  of  the  investigation  are  present.  In  other  words,  they  are 
in  no  wise  limited  in  their  field  of  research.  If  scientific  in  character, 
however,  they  must  possess  distinct  features  in  common  wherever 
applied.  It  is  the  discussion  of  these  common  features,  in  short,  of  the 
method  which  forms  the  subject  of  the  work.    As  a  result,  the  treat- 


History  and  Theory  of  Statistics.  5 

ment  is  not  only  broader,  but  different  from  the  usual  treatment  of 
statistics  to  be  found  in  the  foreign  treatises  on  the  subject,  or  in  the 
monograph  of  Prof.  Smith  above  mentioned.  As  a  rule,  these  treat- 
ises deal  in  statistics  as  our  knowledge  numerically  expressed  of  a 
group  of  phenomena  variously  designated  as  the  state,  society,  human 
communities,  etc.  They  contain  therefore  many  statistical  tables  and 
the  consideration  of  the  conclusions  to  be  drawn  from  the  figures 
presented.  The  discussion  of  methods  occupies  a  minor  place.  To 
Prof.  Meitzen  all  this  is   explanatory  matter,  the  method  itself~Tne~ 


jsence  of  the  subject.  This  view  of  the  matter  enables  him  to  treat 
tTTe~subJect  in  a.  smaller  compass  than  is  customary,  and  further  to 
invest  it  with  a  general  interest,  not  confining  it  to  the  needs  of  econ- 
omists and  sociologists  simply,  but  furnishing  precepts  to  all  who  may 
be  engaged  in  the  collection  or  use  of  figures  for  the  purposes  of  argu- 
ment or  demonstration. 

In  conformity  with  this  conception  of  statistics  the  first  part  of  the 
work  traces  historically  the  growth  of  our  knowledge,  and  processes 
of  thought  in  using  figures,  up  to  the  point  where  it  has  become  possi- 
ble for  us  to  formulate  connectedly  the  underlying  principles,  in  short, 
to  present  a  science  of  statistics  which  should  be  a  science  of  method. 
To  this  end,  it  was  highly  desirable  that  the  presentation  of  the  subject 
should  proceed  in  the  historical  form.  The  reader  is  able  to  follow  in 
the  light  of  this  underlying  conception  with  interest  and  intelligence 
what  might  otherwise  appear  a  recital  of  insignificant  details.  The 
reader  is  forced  to  the  conviction  that  the  unity  of  statistical  effort  is 
to  be  found  nowhere  else  than  in  the  methods  pursued  by  statisticians 
the  world  over.  The  unfolding  of  this  conviction  is  purposed  by 
the  historical  part  of  the  work,  and  thus  the  reader  is  prepared  for 
the  better  appreciation  of  the  theoretical  discussions  which  form  the 
second  part  of  the  work. 

The  theory  of  statistics  to  Prof.  Meitzen  consists  of  the  logical  re- 
quirements of  statistical  proof.  It  is  the  discussion  of  these  elements 
which  forms  the  contents  of  the  theory  of  statistics.  The  mental  pro- 
cesses involved  in  the  statistical  statement  and  the  statistical  argument 
are  carefully  analyzed.  This  analysis  proceeds  to  the  very  minute 
details,  giving  everywhere  a  complete  statement  of  the  nature  which 
logical  necessity  demands  that  they  should  have  in  order  to  fulfil  the 
conditions  of  correct  statement  or  proof.  Thus  the  model  statistical 
argument  is  constructed.  Its  parts  are  analyzed,  their  true  nature 
explained,  the  necessary  connection  between  the  parts  displayed. 
Those  who  are  familiar  with  this  model  argument  are  thus  supplied 
with  tests  which,  applied  to  the  arguments  presented  to  them,  will 
enable  them  at  once  to  discover  their  truth  or  falsity. 

Practical  statistics,  the  work  of  official  bureaus,  is  not  a  matter  of 
drawing  inferences  but  of  collecting  material.    Their  work  is  largely 


6  Annals  of  the  American  Academy. 

preparatory  to  statistical  argument.  Theirs  is  the  technique  of  statis- 
tics. What  demands  does  theory  make  upon  them  ?  The  answer  to 
this  question  forms  the  topic  of  the  third  part  of  the  work.  How 
should  the  bureaus  conduct  their  work  that  the  logical  requirements 
of  the  model  statistical  argument  be  fulfilled  ?  What  light  does  the 
analysis  of  the  statistical  argument  throw  upon  the  workings  of  these 
bureaus  ?  These  are  some  of  the  questions  discussed  in  this  portion 
of  the  work. 

The  unity  of  the  work  rests,  as  is  seen  from  the  above,  in  the  funda- 
mental conception  of  statistics.  The  various  parts  of  the  work  must 
be  read  in  the  light  of  this  conception.  The  result  is  a  harmonious 
grouping  of  the  subject  which  well  justifies  for  it  the  claim  to  the 
name  of  science.  Whether  or  not  this  name  is  accorded  to  it  is  a 
question  after  all  of  small  moment,  provided  that  the  continuity  and 
organic  union  of  the  various  parts  be  fully  recognized. 

If  the  translation  of  the  work  as  a  whole  shall  be  useful  in  the 
formulation  for  science  of  the  canons  of  statistical  thought  its  purpose 
will  have  been  accomplished.  It  is  published  in  parts,  I.  History,  II. 
Theory  and  Technique.     Part  II.  is  to  be  issued  shortly. 

Part  I.,  the  history  of  statistics,  forms  the  contents  of  the  present 
volume.  It  is,  as  above  noted,  preparatory  to  the  theory  which  follows. 
The  thread  of  development  is  carefully  traced,  and  the  reader  is 
conscious  of  the  real  and  important  connection  of  events  which 
follows  from  the  author's  fundamental  conception  of  the  essence  of 
statistical  science.  In  addition  to  this  organic  bond  of  union  with  the 
theoretical  portion  of  the  work,  attention  should  also  be  called  to  the 
fact  that  the  present  volume  contains  one  of  the  most  complete  surveys 
of  statistical  literature  which  is  to  be  found  anywhere.  This  feature 
must  give  it  a  special  value  for  those  seeking  to  inform  themselves  in 
this  line,  and  render  the  book  a  useful  work  of  reference. 

With  the  kind  encouragement  of  the  author,  and  with  the  cour- 
teous permission  of  the  publisher  of  the  German  edition,1  the  work  is 
given  to  the  English  public. 


The  Translator. 
Philadelphia,  October,  1890. 

1  The  original  of  the  work  has  the  following  title-page  : 

Geschichte,  Theorie,  und  Technik  der  Statistik,  von  August  Meitzen,  Dr.  ph., 
Geheimer  Regierungs-Rath  a.  D.,  Professor  an  der  Universitat  zu  Berlin.  Mit 
Tafeln.  Berlin.    Verlag  von  Wilhelm  Hertz  (Bessersche  Buchhandlung),  1886. 


PREFACE    OF   THE    AUTHOR. 


In  the  following  outline  I  have  endeavored  to  give  concise  and  sys- 
tematic expression  to  a  complete  theory  of  statistics  together  with 
many  ideas  drawn  from  experience  in  practical  work.  I  am  con- 
scious that  it  might  have  been  desirable  to  devote  to  the  subject  a 
larger  treatise  and  to  include  the  discussion  of  the  more  important 
problems  of  social  and  political  statistics.  Extensive  literary  obliga- 
tions and  the  pressing  need  of  a  basis  for  my  lectures  have  led  me  to 
prefer  an  outline.  Its  brief,  rather  sketchy  form  seemed  to  me  to  pos- 
sess certain  advantages.  No  more  of  the  customary  apparatus  of 
illustration  has  been  introduced  than  was  deemed  necessary  to  dispel 
the  slightest  doubt  as  to  the  propositions  stated.  It  is  however  my 
opinion  that  no  text-book  can  ever  fully  replace  for  the  student  dem- 
onstrations with  the  use  of  the  actual  statistical  material  itself,  and  the 
consideration  of  questions  arising  from  it. 

The  treatment  is  based  throughout  on  the  conception  of  statistics  as 
a  science  of  method.  I  hold  this  view  to  be  correct,  though  I  lay  no 
greater  stress  upon  it  than  is  expressed  in  §  59.  So  far  as  the  question 
of  the  position  of  statistics  in  the  sphere  of  sciences  does  not  concern 
the  method  nor  the  conception  of  statistics  based  upon  it,  it  becomes 
merely  a  discussion  of  the  definition  of  the  word  "  science  "  and  no  essen- 
tial condition  of  the  theory  is  affected  by  the  answer.  No  teacher  of 
statistics  can  neglect  to  consider  the  requisites  and  some  of  the  results 
of  the  statistics  of  population,  of  political  organization  and  finance,  of 
the  soil  and  agriculture,  of  industry  and  trade,  nor  finally  of  national 
prosperity  and  morality.  Whether  these  subjects  taken  together  are 
to  be  called  the  "  science,"  or  whether  they  are  to  be  regarded  as  the 
field  of  systematic  statistics,  is,  as  shown  in  g  90,  of  merely  formal  con- 
sequence. These  subjects  undoubtedly  form  appropriate  material  for 
connected  treatment,  and  they  are  dependent  on  the  same  methods  of 
investigation. 

In  a  clearly-formulated  conception  of  statistics  as  a  science  of 
method,  I  see  the  possibility  of  realizing  an  object  which  I  consider 
essential,  and  which  I  desire  above  all.  I  hold  it  to  be  of  the  highest 
importance  to  demonstrate  the  logical  character  and  logical  rigor  of 
statistics,  and,  if  possible,  to  make  these  ideas  common  property.    The 

(7) 


io      Annals  of  the  American  Academy. 

§  19.  Further  Development  of  the  Statistics  of  Population. 
\  20.  Extension  of  the  Range  of  Statistical  Problems. 
\  21.  Beginnings  of  Tabular  and  Graphic  Presentation. 

II.  Institutions  for  National  Statistics  on  a  Scientific  Basis. 
$  22.  Necessity  for  Statistics  during  the  French  Revolution. 
\  23.  Bureaus  for  Statistics  in  France. 

§  24.  Statistical  Bureaus  in  Italy,  Spain,  Westphalia,  and  Bavaria. 
§  25.  Foundation  of  the  Prussian  Statistical  Bureau. 
§  26.  Reestablishment  of  the  Prussian  Statistical  Bureau. 

HI.  Limitation  of  the  Field  of  Statistical  Science. 
Vg  27.  Limitation  of  Achenwall's  Statistics. 

\  28.  Elimination  of  Political  Economy,  of  Public  and  Administration  Law. 

§  29.  Elimination  of  the  Geographical  Element. 

§  30.  Separation  of  Practical  Life  Insurance  from  Statistics. 

#  31.  Decline  of  Statistics  as  a  System. 
\  32.  State  of  Official  Statistics. 

IV.  Rise  of  National  Statistics  in  the  Various  Civilized  Nations. 

§  33.  France. 

\  34.  Prussia  and  the  other  German  States. 

§  35.  The  German  Customs  Union  (Zollverein). 

§  36.  Holland,  Luxembourg,  and  Belgium. 

§37.  Austria- Hungary. 

§  38.  Great  Britain. 

\  39.  United  States  of  America. 

§  40.  Denmark,  Norway,  and  Sweden. 

§  41.  Russia. 

§  42.  Switzerland,  Italy,  Spain,  Portugal,  and  Greece. 

V.   Conceptions  of  the  Method  and  Purpose  of  Statistics. 
$  43.  Influence  of  Official  Statistics. 
§  44.  Perfecting  of  Sussmilch's  Statistics. 
§  45.  Pauperism  and  Quetelet's  Work  on  Man. 
§  46.  Conceptions  of  Statistical  Theory. 

D.  The  Development  and  Predominance  of  the  Statistical 

Method. 
I.   The  International  Statistical  Congress. 
§  47.  Occasion,  Organization,  and  Duration  of  the  Congress. 

#  48.  Work  and  Influence  of  the  Congress. 

II.  Modern  Statistical  Practice. 
§  49.  Increasing  Need  of  Statistics  and  Statistical  Offices. 
\  50.  Character  of  Statistical  Work. 

III.  Statisticians  of  Morals. 
\  51.  Idea  of  Constraining  Regularity. 
\  52.  Incompatibility  with  Ethics  and  Psychology. 
\  53.  Solution  of  the  Problem  by  the  Statistical  Method. 


History  and  Theory  of  Statistics.  ii 

IV.   Conceptions  of  Statistical  Theory. 

\  54.  Opposing  Positions. 

\  55.  Conception  of  Statistics  as  Science  of  the  State. 

§  56.  Conception  of  Statistics  as  Science  of  Human  Communities. 

\  57.  Conception  of  Statistics  as  Science  of  Method. 

\  58.  Conception  of  Statistics  as  Applied  Logic. 


PART  SECOND. 

THEORY  AND  TECHNIQUE  OF  STATISTICS. 

Introduction. 

§  59.  Position  of  Statistics  as  a  Science. 

\  60.  Points  of  View  for  the  Theory  of  Statistics. 

#  61.  Relation  of  the  Statistical  Method  to  Logic. 
§  62.  Leading  Thoughts  of  the  Statistical  Method. 

A.  Principles  of  Enumeration. 
/.  Fundamental  Conceptions. 
§  63.  Empirical  Conditions  of  the  Enumeration, 
g  64.  Enumeration  and  Calculation. 
\  65.  Enumeration  of  Things  and  Measurement  of  Qualities. 

#  66.  The  Unit  of  Enumeration. 

\  67.  The  Field  of  the  Enumeration ;  The  Limits  of  Time  and  Space. 

II.   The  Process  of  Enumeration. 
§  68.  Observation  and  Summation. 
\  69.  Substitutes  for  Enumeration,  Calculations,  Estimates,  and  the  Enquetc. 

#  70.  Possibility  of  Error  in  Enumeration. 
$  71.  Peculiarities  of  the  Returns. 

§  72.  Enumeration  of  Units  in  Combination. 
§  73.  Results  of  the  Enumeration. 

B.  Principles  of  Statistical  Judgments. 
/.  Quantitative  Relations. 
$  74.  The  Measure  of  Quantity  from  Analogous  Aggregates. 

#  75.  The  Choice  of  Analogous  Aggregates, 
g  76.  Reduction  to  Common  Terms. 

§  77.  Series,  Maxima,  Minima,  and  Averages. 
\  78.  Results  from  Quantitative  Judgments. 

II.  Causal  Connections. 
I  79.  Requirements  and  Limitations  in  Judgments  of  Causality. 
§  80.  Discovery  of  Causality  through  Functional  Series, 
g  81.  Symptoms  and  their  Application  in  Determining  Causality. 


12  Annals  of  the  American  Academy. 

III.  Probability  and  Regularity, 
$  82.  The  Conception  of  Probability. 

#  83.  Suppositions  Based  on  Similar  Causality. 
§  84.  The  So-called  Law  of  Large  Numbers. 

#  85.  The  Regularity  of  Seemingly  Voluntary  Actions. 
\  86.  Statistical  Regularity. 

C.  The  Form  of  the  Process. 

§  87.  Steps  of  the  Statistical  Investigation. 

g  88.  Predominance  of  Statistical  Materials. 

§  89.  The  Elaboration  of  Systematic  Statistics. 

§  90.  Tendencies  of  Systematic  Statistics. 

$  91.  Problems  of  Systematic  Statistics. 

§  92.  The  Form  of  Questions  in  Systematic  Statistics. 

$  93.  Form  of  Judgments  of  Causality  and  Probability. 

D.  The  Requirements  of  the  Technique. 
7".   The  Problem  and  the  Plan. 
£  94.  The  Separate  Phases  in  the  Technical  Process. 
\  95.  The  Development  of  the  Plan, 
g  96.  Estimates  of  the  Time  and  Cost. 
I  97.  The  First  Draft  of  the  Plan. 
§  98.  Instructions  to  Enumerators. 

II.  Enumeration. 
$    99.  Organization  of  the  Process. 
§  100.  The  Observation  in  Enumeration. 
§  101.  The  Observation  in  Estimates. 
$  102.  Summarizing. 

III.  Examination  of  Returns. 
§  103.  Examination.  Correction,  and  Criticism  of  the  Result. 
§  104.  The  Comparison  with  Analogies. 
§  105.  Reductions  to  Ratios  for  Comparison. 

IV.  Presentation  of  the  Results* 
§  106.  Requirements  of  the  Presentation. 
§  107.  Tabulation. 
§  108.  Graphical  Presentation. 

g  109.  The  Demonstration  of  Quantitative  Judgments. 
£  no.  The  Demonstration  of  Judgments  of  Causality  and  Probability. 
§  ill.  The  Character  of  the  Solution. 

V.  PrpsMtatwtL  and  Application  of  the  Results. 
$  112.  Collection  of  the  Richest  Possible  Materials. 
§  113.  Archives  of  Official  Bureaus. 
\  114.  Applied  Statistics,  Political  Arithmetic. 

Conclusion. 

§  115.  The  Character  of  Statistical  Theory. 

§  116.  The  Work  of  the  Professional  Statistician. 

§  117.  The  Position  of  Statistics  in  General  Culture. 


PART    I. 

THE  HISTORY  OF  STATISTICS. 


INTRODUCTION. 
§  I.   THE   SUBJECT  AND   DEVELOPMENT   OF   STATISTICS. 

We  understand  as  statistics  somewhat  superficially  con- 
sidered an  extensive  range  of  practical  rather  than  theo- 
retical problems.  They  are  characterized  by  the  effort  to 
penetrate  into  the  multitudinous  phenomena  of  political 
and  social  life,  of  nature  and  civilization,  by  the  enumera- 
tion of  characteristic  facts,  by  classification  and  explana- 
tion. 

Among  these  characteristic  facts  are  those  relating  to 
topography ;  to  the  population,  and  its  classes  in  regard  to 
social  rank,  age,  religion,  and  occupation ;  to  births,  mar- 
riages, and  deaths ;  to  the  state  and  its  administration,  its 
martial  force,  its  property,  its  expenditures  and  receipts; 
to  the  territory  in  its  physical  aspects,  its  elevation,  water- 
supply,  climate,  and  fertility ;  to  the  agricultural,  industrial, 
and  commercial  pursuits  of  the  people,  also  to  their 
resources  and  capital ;  and  finally  to  their  strength,  their 
riches,  their  morality,  their  public-spiritedness,  their  social 
and  religious  culture,  and  to  their  enjoyment  of  life  in  its 
outward  manifestations.  All  of  these  facts  are  to  be  ascer- 
tained in  reference  to  actual  status  and  to  changes  in  the 
course  of  time. 

The  scientific  interest  in  the  solution  of  these  problems 
is  double  in  its  character.     It  attaches  in  the  first  place  to 

1 13) 


14  Annals  of  the  American  Academy. 

the  subject,  and  secondly  to  the  process  of  investigation, 
to  the  method. 

The  results  of  such  investigations  are  embodied  in 
various  branches  of  human  knowledge.  They  consist  of 
data  concerning  the  quantitative  and  causal  relations  in 
which  the  objects  observed  have  been  found,  and  in  which 
their  reappearance  may  be  expected.  These  results  are 
sources  of  information  for  various  sciences  when  other 
modes  of  investigation  are  inapplicable. 

Scientific  criticism,  and  therefore  the  theory  of  statis- 
tical science,  concerns  itself  with  the  correctness  of  this 
mode  of  investigation  and  its  development. 

Objects  and  their  relations  are  the  material  with  which 
the  theory  has  to  operate.  The  material  appears  to  be 
indefinite  and  unlimited,  and  to  embrace  all  phases  of 
actual  existence.  We  must  therefore  know  something 
about  it  in  order  to  measure  the  scientific  accuracy  and 
reliability  of  the  means  adopted  to  investigate  it.  In  the 
work  of  investigation,  the  methods  are  gradually  more 
clearly  understood,  and  thus  we  arrive  at  well-defined  prin- 
ciples of  research  which  have  the  value  of  scientific  propo- 
sitions. 

The  development  of  statistical  science  began,  like  that  of 
all  others,  with  a  period  of  unconscious  empiricism.  Later 
the  awakening  scientific  conception  of  the  systematic 
investigation  was  so  dominated  by  the  mass  of  facts 
that  methods  secured  for  themselves  only  gradually  a 
place  in  the  system.  The  question  is  indeed  still  unde- 
cided whether  the  true  contents  of  statistical  science  are 
certain  groups  of  phenomena,  particularly  those  of  human 
communities  (Lebensgemeinschaften),  and  the  method 
simply  the  mode  of  securing  knowledge  in  this  field;  or 
whether,  on  the  contrary,  the  method  with  its  logical  and 
technical  basis  forms  the  true  contents  of  the  science,  the 
objects  serving  simply  as  explanatory  of  the  principles  of 
method,  or  as  examples  of  possible  new  problems. 

From  these  preliminary  considerations   it  is  however 


History  of  Statistics.  15 

evident  that  the  history  of  statistics  cannot  be  an  account 
of  the  results  of  enumerations  obtained  in  the  course  of 
time  for  the  solution  of  statistical  problems.  Its  aim  must 
be  to  point  out  the  ideas  which  have  arisen  in  the  develop- 
ment of  the  science,  and  the  range  of  ideas  and  experi- 
ences from  which  the  demands  made  upon  it  by  criticism 
have  been  finally  answered.  It  must  show  systematically 
the  character  of  the  problems  to  which  statisticians  have 
devoted  their  efforts  and  the  ideas  underlying  their  solu- 
tion. It  must  show  the  progress  of  the  critical  compre- 
hension of  the  value  of  the  results  and  demonstrate  the 
growing  clearness  and  definiteness  of  the  theoretical  and 
Jechnical  requirements.  Undoubtedly  the  history  of  sta- 
tistical science  must  be  a  history  of  statistical  theory  and 
technique. 


A.     EMPIRICAL    STATISTICS    IN    THE    CLASSIC    AND 
MEDIEVAL  WORLD. 

§  2.    THE   OLDEST   CIVILIZED    NATIONS. 

Problems,  such  as  we  to-day  call  statistical,  were  sug- 
gested and  solved  in  the  earliest  periods  of  history.  Prac- 
tical necessity  forced  them  upon  the  rulers  of  peoples  on 
various  occasions.  Concerning  numerous  statistical  under- 
takings definite  testimony  has  been  preserved. 

Egypt :  c.  3050,  Arrangements  for  the  construction  of 
the  pyramids;  2200,  Maps  of  the  country;  1400,  Division 
of  the  land  by  Rameses  II. ;  600,  Registration  by  the  police 
of  all  heads  of  families  (Herodotus  II.,  109,  125,  177). 

Judea:  Census  of  the  population,  estimated  1500  B.  C. 
at  c.  100,000  souls  (Numbers  III.,  49-43) ;  in  2030  B.  C, 
at  c.  3,800,000  (II.  Samuel  xxiv.  9;  I.  Chron.  xxi.  5  ;  xxvii. 
24;  xxiii.  3-5). 

China  :  c.  2300,  Description  of  the  provinces  by  Yuking ; 
1200  B.  C,  Topographical  officials  (Ferd.  Frhr.  v.  Richt- 
hofen,  China.     Berlin,  1877,  Vol.  I.  p.  177). 


y 


16  Annals  of  the  American  Academy. 

Persia :  Messenger  mail,  survey  of  roads,  assessment  of 
real  estate  tax  in  Ionia  (Herodotus  III.,  B;  V.,  49,  52  ;  VI., 
42;  VII.,  21). 

(Moreau  de  Jonnes,  Statistique  des  peuples  de  l'antiquite, 
Paris,  185 1.     M.  Duncker,  Geschichte  des  Alterthums.) 

§  3.    GREECE   AND    ROME. 

The  distribution  of  real  property,  of  classes  of  citizen- 
ship, of  military  and  naval  service,  of  taxes  and  public 
burdens,  and  privileges,  was  arranged  in  many  Greek 
states  in  a  manner  which  presupposed  many  inquiries  of  a 
statistical  nature. 

850.  Lykurgus  divided  the  territory  of  Laconia  into 
39,000  portions,  assigning  to  the  Spartans  9000  portions 
and  to  the  Lacedaemonians  30,000  portions. 

594.  Solon's  tax  census  divided  the  people  into  four 
classes  according  to  the  supposed  returns  from  their 
property  measured  in  wheat,  and  imposed  a  poll  tax  on  the 
alien  residents. 

309.  A  census  in  Athens  showed  a  population  of  21,000 
citizens,  10,000  alien  residents,  and  400,000  slaves. 

(Boeckh,  Staatshaushalt  der  Athener.  2d  Ed.  185 1. 
Buchsenschutz,  Besitz  und  Erwerb  im  griechischen  Alter- 
thum.  Halle,  1864.  Hermann,  Griechische,  Staatsalter- 
thiimer,  1875,98,  7.  Clinton,  De  Graeciae  magnitudine  et 
frequentia,  in  the  Fasci  Hellenici,  Kriiger's  edition,  p.  391. 
M.  Duncker,  Die  Hufen  der  Spartiaten.  Monatsbericht 
der  Berliner  Academie  7,  2,  1881.) 

In  Rome  periodical  enumerations  of  the  population  as 
well  as  investigations  of  property  of  an  exactness  not 
attainable  in  recent  times  existed  from  the  time  of  Servius 
Tullius.  There  were  also  after  Augustus  surveys  of  roads 
and  districts,  assessment  of  real  estate  taxes  in  Italy  and 
the  provinces,  and  later  detailed  official  state  handbooks. 

550.  The  constitution  of  Servius  Tullius  distinguishing 
six  property  classes. 


History  of  Statistics.  17 

435.  The  first  census  in  the  presence  of  the  Censors, 
which  in  the  following  470  years  was  repeated  69  times. 
Births  were  reported  in  the  temple  of  Juno  Lucina,  puberty 
in  that  of  Juventus,  and  deaths  in  that  of  Libitina. 

c.  90  A.  D.  Hygin's  treatise  on  surveys  for  real  estate 
taxes  (in  Auctores  gromatici  of  Lachmann  and  Rudorff  I., 

P.  113)- 

c.    296.   Tabula  Peutingerana  (Philippi   d.  t.   P.   Bonn, 

1876). 

c.  330.  Itinerarium  Antonini  (Tobler's  edition,  1863). 

404.  Notitia  omnium  dignitatum  administrationumque 
(Boeking's  edition,  Bonn,  1839). 

(Niebuhr,  Romische  Geschichte  I.  619,  II.  78.  De  la 
Malle,  Economie  politique  des  Romains  1840.  Theod, 
Mommsen,  Staatsrecht  der  Romer  1876,  I.  207,  II.  304. 
Die  amtliche  Bevolkerungsstatistik  im  alten  Rom,  Hilde- 
brand's  Jahrbuch  fur  Nationalokonomie  und  Statistik, 
1866,  Vol.  I.  p.  82.) 

§  4.    THE    MIDDLE   AGES. 

Taxes,  military  service,  tithes,  and  customs  duties  alone 
gave  rise  to  inquiries  and  records  of  some  degree  of  a 
statistical  character.  Of  those  which  have  been  preserved, 
the  most  important  are  the  land  registers  of  different  coun- 
tries showing  the  number  and  obligations  of  the  holdings, 
something  in  the  same  way  as  a  cataster. 

807.  Caroli  magni  memoratorium  and 

808.  Brevis  capitulorum,  concerning  military  service 
(Monum.   Germ.  leg.  Set.  II.,  Tom  I.,  Berolini,   1880,  pp. 

134,  137)- 

c.  830.  Al-Mamum,  Description  of  the  provinces  of 
the  Khalifate  (Fallati,  Einleitung,  in  die  Wissenschaft  der 
Statistik.     Tubingen,  1844,  p.  125). 

950.  List  of  judicial  districts  and  provinces  of  the 
Emperor  Constantin  Porphyrogeneta  (Ibid.). 

1088.  Domesday  book  of  William  I.  (Gneist,  Englisches 
Verwaltungs  Recht,  1876,  I.  p.  1 16). 


1 8  Annals  of  the  American  Academy. 

1 23 1.  Land  Register  of  Waldemar  II.  (Lappenberg, 
Script,  rer.  Danic.  1792). 

1 241.  Inventory  of  Emperor  Frederick  II.  of  the  crown 
estates  in  Sicily  (v.  Raumer,  Hohenstaufen  1841,  II.  409). 

1327.  Katasto  of  Duke  Charles  of  Calabria  (Quadri, 
Storia  della  Statistica,  Venice,  1824). 

1337.  Landbuch  der  Neumarkt  (Gollmert's  edition, 
1862). 

1358-67.  Landbuch  fur  das  Furstenthum  Breslau-Neu- 
markt  (Stenzel,  1842,  in  the  Bericht  des  historischen 
Sektions  der  schlesischen  vaterlandischen  Gesellschaft). 

1375.  Landbuch  der  Mark  Brandenburg  (Fidicin's  edi- 
tion, 1856). 

1377.  Poll  tax  in  England  under  Edward  III.  and  Rich- 
ard II.  (Pelgrave,  the  Parliamentary  Writs  Collection, 
London,  1827). 

1442.  Salt  tax  in  Sicily  under  Alphonse  I  (Galanti, 
Descr.  geogr.  et  statistica  delle  Sicilie,  1787). 

1460.  De  ritu,  situ,  et  moribus  Germanise  of  Pope 
iEneas  Sylvius  Piccolomini. 

15 15.  Machiavelli,  Ritratti  della  Francia  et  della  Alle- 
magna. 


B.     FROM  THE   BEGINNING  OF  SCIENTIFIC   STATISTICS 
TO  THE  YEAR  1750.  y      ->, 

I.  Comparative  Political  Statistics  (Achenwall's 
Statistics). 

§  5.  statistical  needs  of  the  modern  state. 

All  science  is  based  on  a  practical  art,  but  it  soon  over- 
steps these  limits  in  the~search  for  the  general  connection 
of  things.  Thus  it  becomes  a  system,  and  promotes  in 
turn  practical  purposes  by  means  of  systematic  principles 
which  extend  the  limits  of  our  general  knowledge.     It  is 


History  of  Statistics. 


19 


at  first  simply  a  search  for  a  system,  for  a  logical  concep- 
tion, and  is  developed  and  completed  gradually. 

In  the  beginning,  statistics  considered  as  its  material  the 

(most  urgent  need  of  the  period,  namely  the  knowledge  of 

the  state,  and  as  its  method  comparison,  without,  however, 

possessing  an  exact   sense  of  proportion   nor  a  distinct 

consciousness  of  the  necessity  of  measurements. 

The  stimulus  came  from  the  remarkably  rapid  transfor- 

/t     mation  of  mediaeval  society  into  the  form  of  the  modern 

I  state.     At  the  end  of  the  15  th  century  the  general  longing 

"*  for  order  and  security  gave  monarchy  a  rapidly-increasing 

power.     An   experienced   bureaucracy  took  the  reins  of 

government,  a  standing  army  crushed  out  every  resistance 

to  the  measures  of  the  courts  and  the  administration.    The 

nobility  came  to  prefer  court  life,  official  position,  or  the 

management  of  their  large  estates  to  the  ruinous  feuds  of 

earlier  periods.     Fiscal  necessities  gave  rise  to  the  ideas 

of  "  Kameralistik  "  and  "  Wohlfahrtspolizei  "   (productive 

administration  of  public  property,  and  police  regulations 

for   the  promotion   of   general   prosperity).      Without   a 

knowledge  of  the  state  of  the  country,  its  resources  could 

not  be  developed. 

The  totally  changed  character  of  foreign  relations  was 
another  factor.  In  the  circle  which  surrounded  the  mon-s 
arch  there  was  a  possibility  of  rapid  resolution  and  a  dan- 
gerous secrecy  hitherto  unknown.  Noiseless  preparations 
and  agreements  could  turn  the  whole  power  of  the  state 
suddenly  on  some  unforeseen  aim.  The  intriguing  state 
policy  of  Italy,  there  a  hundred  years  old,  became  the 
common  property  and  the  common  danger  of  Europe. 
^  ^""'Modern  diplomacy  arose  and  with  it  a  fabric  of  distrustful 
mutual  observation.  The  key  to  success  was  cautious, 
considerate  judgment,  based  on  the  best  attainable  infor- 
mation as  to  one's  own  military,  financial,  and  political 
resources,  and  those  of  other  powers.  • 

No  wonder  therefore  that  writers  of  this  period  con- 
ceived the  idea  of  investigating  scientifically  the  elements 


20  Annals  of  the  American  Academy. 

of  strength  and  power  of  existing  states,  and  making  this 
the  subject  of  instruction,  though  the  ways  and  means  of 
such  investigation  might  be  new  and  difficult. 

§  6.    FUNDAMENTAL   WORKS. 

Tl^ejfirstJ^pical  work  in  this  field  was  the  Cosmographia 
of  Sebastian  Muenster  (born  1489  at  Ingelheim,  died  1552 
at  Basle,  a  Franciscan,  but  after  1529  Protestant  professor 
at  Heidelberg  and  Basle).  A  portion  of  the  work  appeared 
in  1536,  the  whole  in  1544.  The  1st  book  describes  the 
world  according  to  Ptolemy;  the  2d,  Ireland,  England, 
Spain,  France,  and  Italy;  the  3d,  Germany;  the  4th,  the 
rest  of  Europe;  the  5th,  Asia;  the  6th,  Africa.  Maps  are 
given  for  all  known  countries  and  they  are  treated  system- 
atically under  the  following  heads :  boundaries,  divisions, 
principal  towns ;  history ;  state  organization,  rulers,  nobles, 
estates,  army,  military  capacity,  church  relations,  laws, 
customs  and  manners ;  and  in  detail  the  chief  cities  with 
their  wealth  and  trade.  , ■ 

In  1562,  Francesco  Sansovino  (born  1521  at  Rome,  died 
1586  at  Venice,  lawyer  and  author)  followed  with  his 
work:  Del  governo  ed  amministratione  di  diversi  regni 
ed  republiche  libri  XXII.  It  treats  of  France,  Germany, 
England,  Spain,  Turkey,  Persia,  Tunis,  Fez,  Poland,  Por- 
tugal, ancient  Rome,  modern  Rome,  Switzerland,  Ragusa, 
Sparta,  Genoa,  Athens,  Lucca,  Venice,  Nuremberg,  and 
Utopia,  i.  e.}  Plato's  republic,  and  gives  in  a  small  compass 
a  concise  and  elegant  description  of  their  public  law  and 
their  customs. 

In  1589  appeared  from  the  pen  of  Giovanni  Botero 
(born  at  Bene,  died  1608,  secretary  of  Cardinal  Charles 
Borromeo,  tutor  of  the  children  of  Duke  Charles  Emanuel 
of  Savoy,  and  an  experienced  diplomatist),  Le  relationi 
universali  divisi  in  quatro  parti,  or  in  the  Latin  edition, 
Relationes  universales  de  viribus,  opibus  et  regimine  prin- 
cipum  Europae,  Asiae   et  Africae.      The   modest   volume 


History  of  Statistics.  21 

with  rich  contents  gives  estimates  in  figures  of  the  areas, 
revenues,  taxes,  military  strength,  and  the  importance  of 
the  commerce  of  the  various  countries. 

In  1614  Pierre  d'Avity,  Seigneur  de  Montmarin  (born 
1572,  died  1635,  serious  and  learned  author  in  usum  del- 
phini),  wrote  under  the  initials  D.  V.  T.  Y. :  Les  etats, 
empires  et  principautees  du  monde,  representes  par  la 
description  des  pays,  moeurs,  des  habitans  richesses  des 
provinces,  les  forces,  les  gouvernements,  la  religion  et  les 
princes,  qui  ont  gouverne  chacun  Etat  Volume  I.  con- 
tains the  account  of  a  circumnavigation  of  the  globe  with 
the  description  of  Asia,  Africa,  and  America;  volumes 
II.-IV.  treat  of  Europe  with  exact  and  useful  data. 

All  these  books  appeared  in  numerous  editions  and  in 
several  languages. 

In  1626  the  book-dealers  Elzevir  in  Leyden,  celebrated 
for  their  editions  of  the  classics,  began  the  publication  of 
the  so-called  Respublicae  Elzeviranae,  consisting  of  34,  and 
later  60  descriptions  of  single  states  by  distinguished 
statesmen  such  as  Jean  de  Laet  (director  of  the  Dutch 
West  India  Company,  died  1649),  Contarini,  Josias  Simler, 
Janotti,  and  others. 

§  7.    STATISTICAL   LECTURES   AND   COMPILATIONS. 

Statistical  studies  were  first  introduced  into  the  Uni- 
versity curriculum  in  1660  at  Helmstedt,  by  Hermann 
Conring  (born  1606  at  Norden,  died  168 1,  well-known 
medical  and  physiological  authority,  physician  in  ordinary 
to  several  princes,  professor  of  the  law  of  nature,  and 
distinguished  polyhistor).  His  lectures  were  published, 
in  1668  by  Poepping,  1675  by  Ph.  Andr.  Oldenburger,  and 
1730  according  to  corrections  left  by  Conring  himself,  by 
Goebel.  His  data  are  drawn  chiefly  from  Botero,  the 
Respublicae  Elzeviranae,  and  J.  A.  de  Thou,  Historiae  sui 
temporis  (1606-1614).  Conring  requires  not  only  a  de- 
scription of  the  bn,   as  he  says,  but  also  of  the  causal 


22  Annals  of  the  American  Academy. 

connection,  6c6rc,  of  Aristotle  distinguished  in  time  and 
space.  He  groups  the  causes  according  to  the  four  Aris- 
totelian principles;  the  causa-  fflatedalis,  the^  people  and 
its  energy,  the  land  and  its  production ;  the  causa  finalis, 
prosperity  and  its  means ;  the  causa  formalis,  the  form  of 
the  state  and  the  mode  of  government;  and  the  causa 
efficiens,  the  actual  ruler,  the  officials,  and  the  estates  with 
their  auxiliaries  and  resources  (V.  John,  Geschichte  der 
Statistik,  1884,  Part  I.  p.  52). 

Lectures  on  the  model  of  Conring's  were  read  in  the 
17th  century  by  Oldenburger  (Geneva),  Herz  (Giessen), 
Bose,  Sagittarius,  Schubart  (Jena),  and  Beckmann  (Frank- 
fort-on-the-Oder).  In  1673  the  last-named  wrote  his  His- 
toria  orbis  terrarum  geographica  et  civilis. 

Thomasius  in  Halle  begins  in  1694  the  list  of  the  so- 
called  "  Kameralisten,"  most  of  whom  besides  teaching 
the  science  of  administration  and  finance  delivered  the 
customary  statistical  lectures.  Among  their  publications 
that  of  Everard  Otto  (in  Utrecht),  Primae  lineae  notitiae 
Europae  rerum  publicarum,  1726,  is  most  widely  known. 
By  far  the  best  work  of  this  period  is  that  of  Thomas 
Salmon,  The  present  state  of  all  nations,  1724. 

§  8.    GOTTFRIED   ACHENWALL. 

The  range  of  ideas  represented  in  these  works  received 
from   Gottfried  Achenwall  a  generally  acknowledged  sci- 
\  entific  form.    He  is  therefore  called  the  father  of  statistical 
j  \science. 

Achenwall  (born  17 19  at  Elbingen,  died  1772),  a  pupil 
-of  Schmeitzel  in  Jena,  began  in  1746  statistical  lectures  at 
Marburg,  and  wrote  in  1748  the  essay  "  Vorbereitung  zur 
Staatswissenschaft  der  europaischen  Reiche  "  upon  being 
called  to  Gottingen.  This  work  became  later  the  intro- 
duction to  his  "  Abriss  der  neusten  Staatswissenschaft  der 
heutigen  vornehmsten  europaischen  Reiche  und  Repub- 
liken  "  (later  Reiche  und  Volker),  published  in  1 749. 


History  of  Statistics. 


23 


In  this  introduction  he  uses  for  the  first  time  the  word 
"Statistik  "  (statistics,  statistical  science).1  Up  to  this  time 
the  word  had  been  merely  suggested  by  Philander  von 
Sittenwald's  statista,  one  versed  in  the  knowledge  of  the 
state,  or  by  the  adjective  use,  rationes  statistics,  by  Olden- 
burger,  1668,  bibliotheca  statistica,  by  Thurmann  in  1701, 
and  the  collegium  statisticum  of  Schmeitzel.  Achenwall 
derives  the  word  from  the  Italian,  ragione  di  stato,  practi- 
cal politics,  and  statista,  statesman. 

Concerning  the  definition  of  statistics,  and  its  scientific 
method  of  investigation,  Achenwall  says :  *'  When  I  con- 
sider a  single  state,  I  discern  a  vast  number  of  things 
actually  to  be  found  therein.  Among  them  are  some 
which  concern  obviously  its  jDrosjp^ritv^either  in  obstruct- 
ing it  or  contributing  to  it.  Such  things  we  might  call 
'  Staatsmerkwiirdigkeiten '  (the  remarkable  things  of  the 
state).  The  totality  of  these  '  Staatsmerkwiirdigkeiten ! 
of  a  kingdom  or  a  republic,  makes  up  its  constitution 
iiK£he  broadest  sense,  and  the  account  of  such  consti- 
tutions of  one  or  more  states ,  is  '  statistik.'  Its  final 
object  is  to  gain  political  wisdom  by  means  of  knowledge 
of  the  various  states*  The  internal  interests  of  the  state, 
the  means  of  increasing  its  wealth,  of  stimulating  popula- 
tion and  riches,  of  promoting  science,  industry,  and  com- 
merce, and  of  improving  the  defects  of  the  constitution, 
may  be  treated  separately  for  each  particular  state.  The 
external  interests  of  the  state,  whether  it  can  dispense  with 
foreign  allies  or  must  seek  them,  whether  it  has  much 
or  little  to  fear  from  foreign  powers,  require  comparisons 
of  the  state  with  all  other  states,  and  cannot  therefore  be 
understood  without  a  knowledge  of  these  foreign  powers."/ 

1  M.  Block  (Traite  de  la  statistique,  p.  9,  note)  tells  us :  "  It  seems  to  have 
been  Brion  de  la  Tour  who  employed  for  the  first  time  the  word  '  statistique '  in 
France.  At  least  he  published  in  1789  Tableau  de  la  population  de  la  France, 
avec  citation  des  auteurs,  au  nombre  de  soixante  douze  qui  ont  ecrit  sur  cette 
partie  de  la  statistique.  According  to  Bachaumont,  '  M6moires  secrets,'  the  econo- 
mists employed  the  word  earlier.  It  was  Sinclair  who  introduced  the  word  into 
England."    (Translator's  note.) 


24  Annals  of  the  American  Academy. 

Achenwall,  however,  treats  only  Spain,  Portugal,  France, » 
Great  Britain,  the  Netherlands,  Russia,  Denmark,  and  j 
Sweden.  He  gives  a  careful  picture  of  each,  of  land  and 
people,  in  seven  distinct  groups  of  questions  :  i.  The  lit- 
erature and  sources  of  information.  2.  The  state,  its  ter- 
ritory and  the  changes  of  the  same.  3.  The  land,  its 
climate,  rivers,  topography,  divisions,  abundance  or  scarcity 
of  products.  4.  The  inhabitants,  numbers  and  character. 
5.  The  rights  of  the  rulers,  the  estates,  the  nobility,  and 
the  classes  of  the  inhabitants.  6.  The  constitution  of  the 
court  and  the  government,  laws,  and  administration  of 
churches,  schools,  and  justice,  industry,  home  and  foreign 
commerce,  currency,  finances,  debt,  army  and  navy.  7.  The 
interests  of  national  life  and  politics,  as  well  as  the  outlook 
for  the  future. 

This  conception  of  the  matter  which  statistics  treats 
coincides,  it  is  obvious,  with  that  of  Conring  and  Muen- 
ster.  ([  Achenwall  limits  his  researches  to  the  collection  of 
materia!  from  the  existing  literature,  does  not  criticise 
either  the  sources  of  the  information  or  the  proofs  of  the 
causal  connections,  but  is  satisfied  with  very  general  polit- 
ical, economic,  and  ethical  reflections.  y-  Nevertheless  the 
short  narrative  is  a  model  of  conciseness,  diligence,  and 

:  lucidity.  The  work  found  such  general  recognition  that 
it  was  translated  into  all  languages.  As  a  consequence, 
all  nations  received  the  word  statistics,  and  with  it  at  the 

:  outset  that  conception  of  statistics  which  was  supported 
by  Achenwall. 

II.  Official  Statistics  (Busching's  Statistics). 

§9.  scientific  demands  leading  to  official  statistics. 

The  literary  treatment  of  the  data  relating  to  the  state 
which  has  just  been  considered  was  far  from  excluding 
the  idea  that  an  insight  into  the  state  of  social  and  political 
affairs  might  be  obtained  by  the  cooperation  of  the  official 


History  of  Statistics.  25 

organs  in  the  collection  of  information  on  sound  scientific 
principles.  The  idea  appeared  as  early  as  the  period  of 
the  Reformation. 

Jean  Bodin  (born  1530  at  Angers,  died  1596,  lawyer  and 
professor  of  public  law  at  Paris)  expresses  it  in  his  "  Six 
livres  de  la  republique."  He  pleads  for  the  reinstatement 
of  the  Roman  census  as  an  adjunct  of  the  police  power,  as 
a  safeguard  against  the  arbitrary  and  usurious  demands  of 
the  tax  farmers,  and  finally  as  a  means  of  information  as  to 
the  number  and  position  in  life  of  the  population.  Similar 
inquiries  are  desired  by  Jac.  Franc.  Lottini  (ambassador  of 
Venice  at  the  court  of  the  Emperor)  in  his  essays  on.  the 
Tesoro  publico,  1600.  ' 

A  remarkable  theoretical  and  technical  insight  into  "the 
statistics  of  population  is  shown  by  Georg  Obrecht  (born 
1547,  died  1612,  professor  at  Strassburg)  in  "  Fiinf  unter- 
scheidliche  secreta  politica "  published  in  1617.  In  the 
essay  "  Eine  sondere  Polezei-Ordnung  und  Constitution, 
etc.,  wie  die  gemeine  Wohlfahrt  zu  vermehren  "  he  pro- 
poses continuous  statistics  of  population  based,  to  be  sure, 
on  very  extended  inquisitorial  privileges  of  the  govern- 
ment organs.  Lists  of  legitimate  and  illegitimate  births, 
marriages,  deaths,  and  guardianship,  as  well  as  the  ages 
of  the  people  in  groups  of  three  years,  could  be  obtained 
by  a  permanent  combination  with  the  collection  of  taxes. 
Data  concerning  moral  deportment  and  for  convicts  con- 
cerning reformation  and  repetition  of  offences  could  be 
obtained  also.  His  propositions  are  accompanied  with 
explanations  as  to  their  application  which  approach  a 
legal  ordinance  in  clearness  and  exactness,  and  contain 
schedules  and  estimates  of  probable  cost.  These  all  reveal 
a  wonderfully-clear  conception  of  the  decisive  factors  in 
practical  statistics.  A  second  essay  gives  the  project  of  a 
law  to  authorize  the  fiscus  to  establish  a  life  insurance  and 
pension  institution  (W.  Roscher,  Geschichte  der  National- 
okonomie  in  Deutschland,  1874,  p.  152). 


26  Annals  of  the  American  Academy. 

Various  statistical  inquiries  were  demanded  also  by : 

1623.  Christoph  Besold  (born  1577,  died  1638,  professor 
in  Tubingen)  in  Synopsis  politicae  doctrinae. 

i656./Veit  Ludw.  von  Seckendorf  (born  1626,  died  1692) 
in  "  Deutscher  Furstenstaat." 

1674.  Joh.  Heinr.  Boeder  (born  1614,  died  1672,  pro- 
fessor at  Strassburg  and  Upsala)  in  Institutiones  political 
II.  10. 

c.  1700.  Gottfr.  Wilh.  Frhr.  von  Leibniz  (born  1646, 
died  17 16)  in  a  project  for  the  Saxon  Society  of  Science. 
(Ed.  Bodemann  in  Preussischen  Jahrbucher,  1884,  Vol.  53, 
p.  378.) 

§  10.  completed  official  investigations. 

,  Among  the  first  official  undertakings  in  which  material 
was  collected  and  treated  statistically  were  the  following : 

1575.  Seventy-five  questions  of  Philip  II.  directed  to  the 
prelates  and  corregidors  of  Spain,  concerning  the  state  of 
their  districts.  The  answers  were  classified  for  the  king's 
use  (L.  von  Ranke,  Fiirsten  und  Volker,  I.  p.  120). 

1 58 1.  Nicol  Froumenteau,  Secret  des  finances,  and 

1586.  Et.  Pasquier,  Recherches  de  la  France,  both  from 
the  books  of  the  state  chamber  of  accounts. 

1 597-1610.  Sully  (born  1560,  died  1 641)  presented  to 
Henry  IV.  official  statements  as  to  the  state  of  the  finances 
and  the  army,  and  proposed  in  1609  a  plan  for  a  compre- 
hensive cabinet  d'etat  et  de  guerre  (Memoires  des  sages 
et  royales  oeconomies  d'estat  de  Henry  le  Grand,  1634. 
Petitot,  Collection  des  memoires  relatifs  a  l'histoire  de 
France;  Series  II.,  Vols.  I.-IX.,  Paris,  1820). 

1622,  1639,  etc.  Registration  of  local  citizenship  every 
twelve  years  in  Wiirtemberg. 

1637.  Status  regiminis  Ferdinandi  in  Austria. 

1645  in  Brandenburg,  1647  in  Hesse,  registration  of  the 
tax  collection  bureaus,  the  peasant  proprietors,  and  men 
of  other  occupations. 


History  of  Statistics.  27 

1665.  Colbert's  statistics  of  trade. 

1 67 5- 1 725.  The  so-called  Etats,  numerous  semi-official 
public  documents. 

1679.  Almanach  royal  de  la  France. 

1684.  Annual  accounts  of  births,  deaths,  and  marriages 
in  all  sections  of  Brandenburg. 

1688.  Louvois,  Depot  de  la  guerre. 

1696  the  English  Parliamentary  Papers  first  appear. 

1697  the  first  enumeration  of  cattle  in  Saxony. 

1699  Louis  XIV.  required  reports  from  the  general  in- 
tendants.  The  dissimilar  and  deficient  returns  are  used  by 
Count  Boulainvilliers,  1727,  in  his  Etat  de  la  France. 

In  1719  Frederick  William  I.  of  Prussia  began  the  semi- 
annual tables  of  population,  occupations,  artisans,  domes- 
tics, houses,  real  estate  holdings  in  the  city  and  country, 
taxes,  city  finances,  etc.,  which  were  arranged  at  a  central 
bureau.  Later  these  tables  were  made  every  three  years 
(R.  Boeckh,  Geschichtliche  Entwickelung  der  amtlichen 
Statistik  des  preussischen  Staates,  1863). 

§11.    FREDERICK   THE   GREAT. 

King  Frederick  II.  of  Prussia  regarded  statistics  from  a 
high  scientific  standpoint  as  a  necessary  methodical  obser- 
vation and  a  continuous  test  of  the  efficacy  of  administra- 
tive measures.  He  extended  the  scope  of  the  tables,  by 
including  data  relating  to  social  state,  nationality,  age, 
deaths  by  months,  and  causes  of  deaths  in  56  classes,  speci- 
fications of  the  agricultural  population  and  property  ac- 
cording to  numerous  classes,  improved  and  settled  terri- 
tory, industrial  pursuits  with  460  classes,  linen  and  woollen 
industry,  mining  and  smelting.  Beginning  with  1747,  de- 
tailed reports  of  trade  distinguishing  70-100  different  wares 
were  prepared;  beginning  with  1748  annual  enumerations, 
population,  175 1,  of  cattle  were  undertaken  and  continued 
regularly  after  1770.  In  1772  a  general  table  of  factories 
was  introduced,  1778  seed  and  harvest  were  reported,  and 


28  Annals  of  the  American  Academy. 

1782  the  number  of  ships.  Besides  these  there  are  numerous 
reports  drawn  from  the  operations  of  the  tax,  justice,  mili- 
tary, and  school  departments.  In  1750  were  commenced 
the  triangulation  of  the  state  and  the  preparation  of  the 
chart  of  the  general  staff,  by  the  Field  Marshal  and  Col- 
onel von  Schmettau.  The  statistical  details  were  collected 
in  general  outline  tables  which  the  king  carried  with  him 
on  his  journeys.  His  personal  examination,  his  interest 
in  the  collection  and  his  use  of  the  results,  his  severity, 
his  acuteness,  and  his  remarkable  topographical  knowledge 
secured  for  these  reports  greater  exactness  than  might 
have  been  expected  considering  the  difficulties  to  be  over- 
come. The  universal  obedience  to  the  royal  wish  was' 
naturally  an  important  factor  in  obtaining  correct  returns. 
(Boeckh,  see  §  10 — Meitzen,  Der  Boden  und  die  landwirt- 
schaftliche  Verhaltnisse  des  preussischen  Staates,  1868. 
Part  I.  p.  10.) 

§  12.    ANTON    FRIEDERICH    BUSCHING. 

The  systematic  publication  of  the  details  of  official 
statistics  jowes  its  origin  to  Anton  Friederich  Biisching.  By 
ffi!s~publication  the  use  of  the  facts  in  scientific  study  be- 
came general,  and  a  mass  of  matter  preserved  which  might 
be  of  much  value  in  later  investigations. 

Biisching  (born  1724  at  Stadthagen,  teacher  in  Copen- 
hagen and  St.  Petersburg,  1754  professor  at  Gottingen, 
1766  director  of  a  Gymnasium  at  Berlin,  died  1793)  wrote 
1754-1792  the  first  ten  parts  of  his  "Neue  Erdbeschrei- 
bung,"  which  however  was  not  completed  until  1807  by 
Sprengel  and  others.  In  1758  he  wrote  a  "  Vorbereitung 
zur  gnindlichen  und  niitzlichen  Kenntniss  der  geograph- 
ischen  Beschaffenheit  und  Staatsverfassung  der  europa- 
ischen  Reiche,"  in  which  he  does  not,  like  Achenwall, 
describe  single  states,  but  seeks  rather  to  compare  the 
different^  states  in  the  main  phenomena  of  political   life. 


History  of  Statistics.  29 

In  1767  he  founded  "das  Magazin  far  Historiographie  und 
Geographie,"  which  appeared  in  23  parts  down  to  1793. 
Here  were  collected  statistical  figures  from  numerous  Ger- 
man and  other  lands,  so  that  it  may  be  considered  as  the 
first  periodical  work  on  statistics. 

The  importance  of  Btisching  as  compared  with  Achen- 
wall,  is  chiefly  that  the  former  instead  of  indulging  in 
general  reflections  and  observations,  and  being  content 
with  the  totals,  directed  his  attention  to  the  details.  This 
led  to  a  careful  examination  as  to  the  completeness  and 
correctness  of  the  data,  and  promoted,  by  the  scrutiny  of 
their  origin  and  arrangement,  the  progress  of  critical 
methods. 

III.  Statistics  of  Population  (Sussmilch's  Statistics).     hz> 

§   13.    CONNECTION   WITH    THE   CHURCH    REGISTERS. 

In  a  limited  field  the  statistical  details  had  attracted  at 
an  early  date  the  attention  of  investigators.  These  studies 
had  for  their  subject  the  typical  relations  of  human  ljfe  and 
death,  and  extracted  the  materials  almost  exclusively  from 
the  church  registers. 

Regular  and  continuous  registration  of  births,  marriages, 
and  deaths  was  first  introduced,  as  far  as  is  known,  in 
Augsburg  in  1501,  and  then  in  several  German  cities.  It 
was  prescribed  generally  but  ineffectually  in  1524  by  the 
Synod  of  Seez  in  Alencon,  where  the  Huguenots  were  • 
numerous.  In  1533  the  Brandenburg-Nurnberg  evan- 
gelical Church  Ordinance  required  baptismal  and  marriage 
registers,  and  that  of  Liegnitz  in  1534  baptismal  records. 
Henry  VIII.  in  1537  and  Francis  Lin  1539  ordered  church 
registers  to  be  kept.  In  Breslau  registers  were  ordered  in 
1542  for  marriages,  1570  for  baptism,  and  1599  for  deaths, 
the  same  in  Brandenburg  in  1573,  and  in  the  Electorate  of 
Saxony  in  1580  (A.  L.  Richter,  Die  evangelischen  Kirchen- 
Ordnungen  des   16.     Jahrhunderts,   1846.     E.  Rehnisch, 


30  Annals  of  the  American  Academy. 

Graetzer,  Halley,  und  Neumann,  in  Gottinger  Gelehrten 
Anzeigen,  1883,  p.  1576). 

^In  London  baptismal  records  were  introduced  in  1550, 
and  in  consequence  of  the  plague,  death  registers  in  1592. 
From  1629  women  were  employed  to  inspect  the  dead. 
They  were  required  to  estimate  the  probable  age,  and  to 
register  this  with  a  statement  of  the  illness  or  accident 
causing  death.  The  results  were  published  weekly. 
V  John  Grauntfborn  1620,  died  1674,  shopkeeper,  musician, 

member  of  the  Academy)  compared  and  criticised  these 
figures  for  the  years  1629  to  166 1  in  his  work  "Natural 
and  political  observations  upon  the  bills  of  mortality, 
chiefly  with  reference  to  the  government,  religion,  trade, 
growth,  air,  diseases,  etc.,  of  the  city  of  London,  by  Cap- 
tain J.  G."  It  was  presented  in  1662  to  the  newly-founded 
Royal  Society.  Graunt  comes  to  the  surprising  result  that 
the  sexes  are  nearly  equal  in  numbers,  that  herein  war  and 
pestilence  exercise  no  appreciable  effect,  that  14  boys  are 
born  for  every  13  girls,  and  that  the  ratio  of  births  to 
deaths  is  quite  uniform.  He  calculates  that  of  100  persons 
born,  36  die  in  the  next  6  years,  24  in  the  next  decade,  15 
in  that  following,  and  then  successively  9,  6,  5,  4,  2,  and  1, 
and  demonstrates  finally  that  from  this  ratio  of  deaths  the 
number  of  living  persons  could  be  calculated  (G.  F.  Knapp, 
Theorie  des  Bevolkerungswechsels,  1874,  pp.  57  and  121. 
John,  see  §7).  Graunt's  discoveries  excited  the  greatest 
interest,  and  particularly  the  large  population  which  he 
ascribed  to  London  aroused  the  jealousy  of  Paris  and  led 
'to  further  discussions  and  investigations. 

William  Petty  (born  1623,  died  1687,  physicist,  physi- 
cian, the  friend  of  Hobbes)  in  particular  espoused  the 
cause.  His  chief  work  of  1679  is  "Political  Arithmetick, 
j\  or  a  Discourse  concerning  the  Extent  and  Value  of  Lands, 
^yV  People,  Buildings;  Husbandry,  Manufacture,  Commerce, 
Fishery,  Artizans,  Seamen,  Soldiers;  Public  Revenues, 
Interest,  Taxes,  Superlucration,  Registries,  Banks;  Valua- 
tion of  Men,  Increasing  of  Seamen,  of  Militia's,  Harbors, 


History  of  Statistics.  31 

Situation,  Shipping,  Power  at  Sea,  etc.  As  the  same  relates 
to  every  country  in  general,  but  more  particularly  to  the 
Territories  of  His  Majesty  of  Great  Britain,  and  his  Neigh- 
bors of  Holland,  Zealand,  and  France."  He  complains  in 
it  of  the  lack  of  figures  based  on  actual  enumeration  and  says 
of  his  method.  "  I  have  taken  the  course  to  express  myself 
in  Termsj^Number,  Weight,  or  Measure,  to  use  only 
Arguments  of  Sense  and  to  consider  only  such  Causes  as 
have  visible  Foundations  in  Nature."  His  posthumous 
works  were  published  in  1690  and  1699  by  John  Williamson. 
In  1696  Gregory  King  calculated  from  the  hearth  tax, 
assessed  in  1690  on  1,319,215  houses,  the  population  of 
England  at  five  and  a  half  million  souls.  Numerous  simi- 
lar calculations  are  to  be  found  in  the  Philosophical  Trans- 
actions of  this  period. 

§  14.    EDMUND   HALLEY'S    MORTALITY   TABLES. 

In  order  to  prove  that  it  was  superstitious  to  ascribe  any 
special  importance  to  the  seventh  and  ninth  year  for  the 
expectation  of  life,  the%  prebendary  Caspar  Neumann  of 
Breslau  collected  from  the  parish  registers  of  the  city,  in 
the  years  1687-91,  notes  of  5869  deaths,  from  which  he 
counted  those  falling  in  the  fateful  years  and  those  lying 
between.  These  figures  and  the  notes  on  which  they  were 
based  came  into  the  possession  of  the  Royal  Society  in 
1692,  as  it  appears  through  the  intervention  of  Leibnitz. 
The  Society  asked  Halley  for  an  expression  of  opinion  on 
them. 

Edmund  Halley  (born  1656,  died  1742),  who  made  at  St. 
Helena  in  1676  a  catalogue  of  the  stars  of  the_southern 
heavens,  and  calculated  in  1681  the  comet  bearing  his 
name,  made  in  1693  a  report  which  was  printed  in  the 
Philosophical  Transactions  of  the  Royal  Society  for  that 
year  (Vol.  XVII.,  Nos.  196  and  198)  under  the  title  "An 
Estimate  of  the  Degrees  of  Mortality  of  Mankind,  drawn 
from  curious  Tables  of  the   Births  and  Funerals  at  the 


32  Annals  of  the  American  Academy. 

City  of  Breslaw ;  with  an  Attempt  to  ascertain  the  Price 
of  Annuities  on  Lives."  In  this  he  gives  in  the  form  shown 
in  Appendix  L,  Halley's  mortality  tables,  which  were  the 
earliest  apart  from  the  figures  given  by  Graunt. 

Though  his  methods  of  calculation  even  with  the  light 
thrown  on  them  by  the  papers  preserved  by  the  Royal 
Society  are  obscure,  his  figures  are  gained  essentially  by 
eliminating  from   Neumann's  figures  apparent  accidental 
variations,  and  developing  from  the  deaths  at  the  various 
ages  a  general  scale.     On  the  basis  of  the  ages  of  those^ 
who  die  he  shows  how  many  of  a  certain  number,  born  in 
a  given  year,  will  die  or  survive  in  each  succeeding  year. 
From  this  he  calculates  for  vlifejiisjirance  the  average  ex- 
pectation of  life  at  each  age,  and  for  the  statistics  of  popu-  / 
lation  the  probable  number  of  the  population  of  a  given  \ 
district  from  the  number  of  births  in  a  year.  ^ 

However,  Halley  erred  in  the  hopes  whjch  he  expressed 
of  the  reliability  of,  such  calculations  from  his  figures.  He 
himself .. limits  their  applicability,  in  pointing  out  that  they 
would  not  be  exact  for  cities  such  as  London  and  Dublin, 
on  account  of  the  continual  changes  of  trade.  Though  he 
speaks  of  an  excess  of  births  over  deaths  he  does  not 
notice  that  his  figures  apply  only  to  a  stationary  popula- 
tion, which  neither  increases,  nor  decreases  in  the  course 
hoLaJluman  life.  If  the  yearly  increase  of  population  in 
» Europe  be  assumed  to  be  on  an  average  one  per  cent., 
it  is  evident  that  those  who  die  at  the  age  of  100  would 
come  from  a  smaller  population,  in  fact  about  2.7  times 
less,  than  that  of  the  children  of  one  year.  \\  The  percent- 
ages, therefore,  which  are  calculated  from  the  various  ages, 
from  the  deaths  of  one  year  or  of  several,  without  consid- 
eration of  the  increase  of  population,  must  undoubtedly  be  ' 
incorrect  somewhere  in  the  table,  either  at  the  beginning 
or  at  the  end.  According  to  Halley,  the  average  length  of 
life  is  only  about  31  years,  whereas  counting  I  percent, 
annual  increase  it  would  be  37.5  years. 

In  how  far  the  mode  of  calculation  which  Halley  em- 


History  of  Statistics.  33 

ployed  is  original  with  himself  we  do  not  know.  His 
contemporaries  recognized^  him  as  the  founder  of  this 
method  of  calculating  mortality  tables,  which  however  is 
only  applicable  to  a  stationjuxj^pulation  (Knapp,  p.  61, 
see  §  13).  C^2f  . 

§  15.   ANNUITY   AND   LIFE   INSURANCE   INSTITUTIONS. 

Life  insurance  was  known  in  the  Middle  Ages  for  per- 
sons going  on  sea  voyages_or^pilgrimages.  Out  of  it  grew 
a  species  of  wager  on  one's  own  or  another's  life,  which  as 
being  questionable  was  forbidden  in  1570  in  Holland,  in 
1598  in  Genoa,  in  168 1  in  France,  though  permitted  in 
England  up  to  1773. 

During  the  17th  century  the  games  of  hazard  grew  into 
prominence.  In  1660  lotto  was  invented;  1634-37  was 
the  period  of  the  tulip  swindle  in  Holland;  and  in  1653 
France  accepted  the  project  of  the  physician  Lorenzo 
Tonti,  to  contract  State  debts  by  selling  annuities  in  the 
tontine  form,  whereby  the  income  of  the  dying  accrued  to 
the  surviving.  The  probable  duration  of  the  annuities 
having  been  calculated  too  short,  the  state  drew  little 
profit  from  them,  and  supplied  their  place  with  lotteries 
(Bender,  Die  offentliche  Gliickspiele,  1862).  In  1657  Ch. 
Huygens,  and  in  1660  Format  and  Pascal  calculated  the 
probabilities  in  games  of  chance.  In  1670  Jean  de  Witt 
(executed  1672)  formulated  the_j?rinciples_for  annuity  life 
insurance  from  the  death  registers  of  Dutch  cities.  In_ 
1698  the  first  life  insurance  institution  was  founded  in 
London  on  Ascheton's  plan,  and  in  1699  the  Society  of 
Assurancy  for  Widows  and_Orphans.  Both  existed  up  to 
1730.  In  1706  the  Amicable  or  Perpetual  Assurance  was 
founded  in  London,  which  in  1866  ceded  its  business  to 
the  Norwich  Union;  1721  saw  the  foundation  of  the 
Royal  Exchange  and  the  London  Assurance  Company, 
both  of  which  exist  at  present. 

In  17 1 3  there   appeared  by  Jac.  Bernoulli  (born  1654,, 
3 


34  Annals  of  the  American  Academy. 

died  1705,  professor  in  Basel)  "  Ars  conjectandi,"  a  scien- 
tific demonstration  of  the  theory  of  probabilities. 

More  exact  calculationslJfTrfortality  were  furnished  in 
1724  by  de  Moivre  (born  1667,  died  1754,  Huguenot,  Lon- 
don) Annuities  of  lives;  1737  to  1748  by  W.  Kerseboom 
(born  c.  1 691,  died  177 1,  Hague,  treasury  official)  in  vari- 
ous essays  in  which  as  he  says  he  follows  Halley's  method, 
but  whose  defects  he  points  out  (Knapp,  p.  60,  see  §  13); 
also  in  1740  by  Nicol  Struyk,  who  for  the  first  time  calls 
attention  to  the  different  mortality  of  men  and  women. 

§  16.  johann  peter  sussmilch. 

The  investigations  of  the  course  of  human  life,  which 
had  hitherto  been   carried  on  in  England,  Holland  and  t 
France  from  mathematical,  political  and  industrial  points    ( 
of  view,  were  taken  up  first  in  Germany  by  Sussmilch, 
who  placed  them  under  the  more  comprehensive  and  more 
ideal  standpoint  of  scientific  statistics. 

Joh.  Peter  Sussmilch  (born  1707  at  Berlin,  died  1767, 
military  chaplain,  Qberkonsistorialrath,  member  of  the 
Academy)  wrote  "  Betrachtungen  iiber  die  gottliche  Ord- 
nung  in  den  Veranderungen  des  menschlichen  Geschlechts 
aus  der  Geburt,  dem  Tode,  und  der  Fortpflanzung  desselben 
erwiesen,"  dated  1741,  on  the  march  to  Schweidnitz,  and 
provided  with  a  preface  by  Chr.  Wolff.  (The  same  in 
1742.) 

He  rests  his  work  on  the  authority  of  Graunt^Petty, 
King,  Arbuthnot,  Derham.  Niuwentyt,  and  upon  the  new 
and  rich  material  for  the  Prussian  provinces.  For  the 
regularity  of  the  movement  of  the  population  of  middle 
Europe  he  calculates  averages  which  are  substantially 
correct  tothe  present.  In  these  results  he  perceives  a 
providential  ordinance  (Genesis  i.  28),  contrary  to  which 
mankind  cannot  act  with  impunity.  He  proves  the  birth 
of  21  sons  for  20  daughters,  and  the  /equality  of  the 
sexes  at  the  age  of  marriage,  from  which  he  derives  the 


History  of  Statistics.  35 

I 
■command  of  monogamy.      The  higher  order  of  things\ 

reveals  itself  further  in  the  fact  that  in  each  year  about 
the  same  number  die  as  in  every  other,  and  this  applies 
alike  to  children,  youths,  men,  and  old  men  and  to  the  two 
sexes  alike,  that  sickness  and  epidemics  do  not  essentially 
alter  these  relations,  and  also  that  multiple  births,  still- 
births, and  accidents  have  certain  numerical  relations. 
For  the  order  of  decease  he  takes  Riciotti's  estimate  of 
1000  millions  as  the  population  of  the  globe,  and  describes 
it  under  the  metaphor  of  a  body  of  passing  troops.  The 
first  detachment  of  children  from  birth  up  to  5  years  of 
age  consists  of  something  over  108  millions,  those  of  5 
to  10  years  65,  those  from  10  to  15  years  62,  those  from 
15  to  20  years  60  millions,  etc.  Alwa^s^Jhowjever,  when 
10  die  13  newly-born  begin... their. course,  and  each  age 
furnishes  a  fixed  contingent  of  deaths. 

He  does  not  doubt  that  the  order  thus  created  by  the 
will  of  God  can  be  disturbed  by  outward  circumstances 
and  wilful  acts.     He  finds  a  proof  of  this  in  the  fact  thatK 
in  c7ties~one  person  dies  out  of  every  25  to  32  ;  in  the  coun-j 
try,  however,  one  out  of  every  40  to  45.     He  censures/ 
therefore,  with  earnestness  all  unnaturalness,  immorality, 
and  luxury  of  life.     In  want,  waste,  wars,  and  worthless  \ 
constitutions,  he  perceives  a  source  of  unnatural  and  un-    \ 
sound  conditions  whose  prevention  by  all  legitimate  means      j 
is  the  duty  of  the  state.     Here  he  stands  upon  the  stand-<^"' 
point  of  the  most  enlightened  p^Hticians_of  his  time.    The 
second  edition  of  176 1  recommends  expressly  the  emanci- 
pation of  the  person  and  the  real  property  of  the  peasant, 
the    abolition   of  feudal  burdens,  the  cultivation  of  wild 
lands,  protection   against  filling   up  with    sand   or  other >*^y^ 
waste,  proper  distribution  of  the  field  holdings,  renting 
of  the  public  domains,  the  use  of  oxen  instead  of  horses, 
fruit  and  bee  culture,  encouragement  of  manufactures  and 
trades,  especially  such  as  require  much  labor,  encourage- 
ment of  commerce   by  reliable  wares,  reasonable  prices 
and   freedom  from  burdensome  taxes.     To  work  in  law 


36  Annals  of  the  American  Academy. 

and  ordinance  from  the  points  of  view  shown  to  be  bene- 
ficial for  the  welfare  of  the  population,  is  the  occupation  of 
the  ruler  and  his  God-appointed  duty. 

Sussmilch  does  not  discuss  the  mathematical  basis  of 
the  order  of  mortality,  although  he  is  familiar  with  the 
standpoint.  He  emphasizes  the  necessity  of  proper  calcu- 
lations for  annuities  and  life  insurance. 


C.  DEVELOPMENT  OF  UNIFORM  SCIENTIFIC  STATISTICS. 
I.  Broader  Views  and  Problems. 

§  17.    THE   SCHOOL   OF   ACHENWALL. 

N 

About  the  middle  of  the  eighteenth  century  the  various 
lines  of  statistical  activity  which  had  appeared  found 
almost  contemporaneously  distinguished  representatives — 
men  who  systematized  and  broadened  the  field.  These 
men  belonged  exclusively  to  Germany  and  lived  in  Got- 
tingen  and  Berlin,  not  without  personal  relations  to  each 
other,  yet  without  scientific  connection  or  cooperation. 
Each  had  a  circle  of  pupils  and  successors,  and  these  in 
turn  remained  for  a  long  time  in  the  traditional  ways.       ^^ 

Acliejiwall  was  able  to  bring  his  fifth  edition  of  1772  in 
accord  with  the  latest  data.  The  sixth  was  edited  by  A.  L. 
v.  Schlozer  in  1781,  the  seventh  in  1790  by  Sprengel. 

Among  the  works  of  the  school  may  be  named — 

1757.  Reinhard,  Einleitung  der  vornehmsten  Reiche  und 
Republiken  in  Europa  and  Africa. 

1 76 1.  Baumann,  Kurzer  Abriss  der  Statistik. 

1772.  Meusel,  Lehrbuch  der  Statistik. 

1773.  Gatterer,  Ideal  einer  allgemeinen  Weltstatistik 
(with  a  history  of  the  literature). 

1782.  v.  Hertzberg,  Reflexions  sur  la  force  des  etats,  and 


History  of  Statistics.  37 

1785.  Sur  la  population  des  etats  en  general  et  sur  celle 
des  etats  Prussiens  en  particulier. 

1787.  Antonio  Mont  Palau,  Description  politica  de  las 
soberanies  de  Europa. 

1787.  Ed.  Zimmermann,  Political  Success  of  the  present 
state  of  Europa. 

1792.  M.  de  Beaufort,  Grande  portefeuille  politique. 

Grundrisse  der  Staatskunde,  were  written  in  1792  by 
Liiders,  in  1793  by  Sprengel,  in  1796  by  Luca,  in  1797  by 
Fabri,  and  in  1805  by  Mannert.   - 

The  most  influential  pupil  of  Achenwall,  August  Ludwig 
v.  Schlozer  (born  1735,  died  1809,  official  at  St.  Petersburg, 
professor  at  Gottingen),  wrote  in  1804  "Theorie  der  Sta- 
tistik  nebst  Ideen  iiber  das  Studium  der  Politik  iiberhaupt." 
The  plan  of  his  theory  is  arranged  as  follows ;  vires  (re- 
sources, soil,  money),  unites  (form  of  the  state  and  the 
administration),  agunt  (influences  and  effects).  History  is 
for  him  continuous  statistics,  statistics  stationary  history. 
(Th.  Zermelo,  Aug..  Ludw.  v.  Schlozer,  ein  Publizist  im 
alten  Reich,  1875.) 

'  §  l8.    CONTINUATION   OF   OFFICIAL   STATISTICS. 

In  the  bureaucracy  and  finance  administration  of  all 
states,  statistical  matter  covering  a  large  field  was  collected 
and  considered  necessary,  but  seldom  published.  But  little, 
therefore,  of  it  is  known.  """ 

Enumerations  of  the  population  took  place :  in  Hesse- 
Darmstadt,  1742,  70,  88,  91  et  seq.;  Hesse-Cassel,  1747, 
7$,%\,et  seq.;  Gotha,  1754  et  seq.  annually  ;  Saxony,  1755, 
72,  83,  90;  Hannover,  1755  ;  Brunswick,  1756,  60,  88,  90; 
Denmark,  1769,  87;  Bavaria,  1777;  Mecklenburg-Strelitz, 
1784;  German  Austria,  1785;  Spain,  1787;  the  two  Sici- 
lies, 1788  ;  Savoy  and  Nice,  1789.  In.  North  America  the 
decennial  census  provided  for  in  the  constitution  was  car- 
ried out  for  the  first  time  in  1790.  In  France  a  census  of 
hearths  was  taken  by  the  Due  d'Argenson  in  1753. 


\ 


38  Annals  of  the  American  Academy. 

Finance  Statistics  were  published  for  Prussia,  1780,  by 
v.  Hertzberg,  "  Huit  dissertations,"  for  France  by  Necker, 

178 1,  "  Compte  rendu  au  roi." 

General  statistics  of  countries  were  published  for  the 
two  Sicilies  by  Galanti,  Descriptione  geographica  et  sta- 
tistica  delle  Sicilie,  1 787-1 791;  and  for  Tuscany  Governo 
della  Toscana  sotto  il  regno  de  Leopoldo  II.  1790;  for 
Spain  by  Larruga,  Memoires,  1790-1797. 

Collections  of  materials  were  published  as  follows  :  Aug. 
Ludw.  v.  Schlozer,  "  Briefwechsel,"  60  pamphlets,   1775— 

1782,  continued  till  1794  as  "  Staatsanzeiger,"  with  the  co- 
operation of  Count  Carmer  v.  Hertzberg,  Count  Firmian, 
Duke  of  Saxe-Meiningen,  and  other  prominent  statesmen  ; 
Dohm,  Materialien  zur  Statistik  der  neuesten  Staatenge- 
schichte,  1777-85;  Le  Bret,  Magazin  zum  Gebrauch  der 
Staaten  und  Kirchengeschichte,  10  parts,  1781-88. 

State  Almanacs  appeared  from  1700  on  for  the  Nether- 
lands, from  1704  for  Prussia,  from  1720  at  Ratisbon,  from 
1728  for  the  Electorate  of  Saxony,  from  1730  the  royal 
calendar  in  England,  from  1736  at  Frankfort-on-the-Main, 
from  1740  the  Almanach  de  Gotha,  from  1775  for  Meck- 
lenburg. 

Von  Schlozer  praises,  in  1806,  the  new  era  of  things  in 
regard  to  publications,  "  How  fortunate  we  statisticians  of 
the  new  century,  the  disgraceful  distinction  between  uni- 
versity and  cabinet  statistics  has  ceased  to  exist." 

§  19.    FURTHER    DEVELOPMENT   OF   THE   STATISTICS    OF 
POPULATION. 

,  Sussmilch  had  not  gathered  like  the  rest  a  circle  of 
pupils  (the  third  edition  of  his  work  was  published  by  Ch. 
J.  Baumann,  1790),  yet  the  movement  of  population  re- 
mained the  subject  of  much  attention. 

Upon  the  proposal  of  Menajider,  Sweden  commenced  in 
1 74 1  the  registration  in  all  parishes  of  births,  marriages, 
and  deaths.     The  results  were  arranged  by  the  Academy 


History  of  Statistics.  39 

in  a  work  of  Tables,  beginning  1749,  which  were  made 
the  subject  of  scientific  treatment  in  1765-82  by  War- 
gentin.  (Knapp,  p.74.  See  §  13.  Memoires  de  1'  academie 
des  sciences  de  Suede,  trans,  by  Kastner,  1767.) 

Simpson  in  1742,  Deparcieux  1746,  Deslandes  1750,  fur- 
nished calculations  of  mortality. 

Euler  (born  1 707,  died  1783)  wrote  Calcul  de  la  proba- 
bility dans  le  jeu  de  rencontre,  and  demonstrated  in  1753 
the  means  of  correcting  Halley's  tables  on  the  basis  of  the 
average  growth  of  population. 

n  1765  the  Equitable  Life  Insurance  Institution  on  the 
mutual  principle  was  founded  at  London. 

Methods  of  calculation  were  made  more  exact  by  Price, 
1771 ;  Morgan,  1779;  Tetens,  1786,  and  finally  through  the 
method  of  smallest  squares  by  Friederich  Gauss  (born 
1777,  died  1855). 

Condorcet  (born  1743,  died  1794)  maintains  in  his  "  Es- 
quisse  d'un  tableau  historique  des  progres  de  l'esprit 
humain,"(tiiat  human  actions  can  only  be  conceived  as 
happening  accordingjto  the  materialistic  laws  of  nature.  \ 

Y*^§  20.    EXTENSION    OF   THE   RANGE   OF   STATISTICAL   PROBLEMS. 

The  mere  continuation  of  the  chief  lines  of  statistical 
thought  hitherto  considered  does  not,  however,  exhaust 
the  development  of  the  science  in  this  period.  Numerous 
methods  of  observation  and  ideas  were  suggested,  which 
seemed  to  show,  on  the  contrary,  that  the  range  of  subjects 
and  ideas  was  capable  of  a  very  considerable  extension. 
In  a  certain  sense  this  may  be  termed  a  period  of  dis- 
covery in  this  field.  Among  characteristic  works  may  be 
mentioned — 

(a)  On  Population :  Messance,  Recherches  sur  la  popu- 
lation de  quelques  provinces  et  villes  du  royaume  avec  des 
reflexions  sur  la  valeur  du  bled  tant  en  France  qu'en  An- 
gleterre  *depuis  1674,  j usque,  1764,  1766,  and  Nouvelles 
recherches  sur  la  population  en  France  avec  des  remarques 


40  Annals  of  the  American  Academy. 

sur  divers  objects  de  V  administration,  1788,  concerning 
Athe  effect  of  the  price  of  grains  and  other  contemporary 
\!bonditions  and  measures  upon  the  population.  *v  Moheau, 
Recherches  et  considerations  sur  la  population  pVla  France, 
1778  (assisted  by  Montyon).  De  la  Pommelles,  1789,  Re- 
cherches statistiques  sur  la  population  de  la  France,  concern- 
ing the  results  of  the  levy  of  troops.  Th.  Rob.  Malthns 
(born  1766,  died  1834,  clergyman,  professor  of  political 
economy),  Essay  on  the  principles  of  population,  1798; 
population,  according  to  his  view,  increasing  in  a  geo- 
metrical, the  means  of  subsistence,  on  the  other  hand,  in 
an  arithmetical,  progression,  the  danger  of  over-population 
is  produced. 

(b)  On  Agriculture:  Arthur  Young(bom  I74i,died  1820, 
merchant  ancPagriculturalist),  Political  Arithmetic,  1774; 
Economic  voyages  in  England,  France,  Spain,  Italy,  15 
vols.,  1768-1795  ;  Annals  of  Agriculture,  45  vols.,  1784 
et  seq. 

(c)  On  Commerce:  Raynal,  Histoire  philosophique  et 
politique  des  etablissements  et  du  commerce  des  Euro- 
peens  dans  les  deux  Indes,  177 1.  Seitwein,  Anfrage  an  das 
deutsche  Publikum,  die  Handelsbilanz  zwischen  England 
und  Deutschland  betreffend,  1773.  K.  v.  Sttuensee  and  J. 
C.  Sinaphis,  Kurz  gefasste  Beschreibung  der  Handlung  der 
vornehmsten  europaischen  Staaten,  1 778-1 782.  A.  R.  W. 
Crome,  Europas  Produkte,  1782.  De  Tolosan,  Memoires 
sur  la  commerce  de  la  France  et  ses  colonies,  1798.  J.  A. 
Noack,  Statistischer  Versuch  iiber  die  Handelsbilanz 
zwischen  Deutschland  und  Frankreich,  1794. 

(d)  On  Taxes :  Mauvillon  (Mirabeau),  Monarchic  Prus- 
sienne,  1788. 

(e)  On  Churches :  Schonemann,  Grundriss  einer  Statistik 
des  deutscnen  Religions-  und  Kirchenwesens,  1797. 

(/)  On  Civilization  in  general:  Due  oV  Argenson,  Con- 
siderations~sur  la  gouvernement  ancien  et  present  de  la 
France,  1765. 


UNtVEKSrnr 

History  of  Statistics.  41 

§21.  beginnings  of  tabular  and  graphic  presentation. 

With  the  endeavor  to  establish  causal  connections  the 
statistical  argument  turned  more  and  more  toward  the 
proof  by  numbers  and  away  from  descriptions  and  opin- 
ions  of  a  general  character.  The  excess  and  diminution, 
M\e  rise  and  falFoT  the  rows  of  figures  became  the  means 
/of  measurement  and  proof.  This  means  had  a  value  of  its 
own  of  the  utmost  importance  for  the  investigations.  Here, 
therefore,  are  the  first  steps  toward  a  further  progress  in 
the  method. 

As  early  as  174 1  Acherson,  a  Dane,  had  attempted  in 
his  Description  statuum  cultiorum  in  tabulis,  to  portray  the 
most  important  features  of  the  European  states  in  tables 
of  figures  only.  His  data  embrace  area,  population,  re- 
ligion, finances,  armies,  the  political  constitution,  money, 
weights  and  measures!  As  long,  however,  as  only  highly 
unreliable  and  defective  figures  could  be  obtained,  such 
efforts  could  not  be  crowned  with  success. 

Even  in  1782  little  attention  was  paid  to  the  idea  of 
Crome  in  Giessen,  who  proposed  to  present  the  results 
graphically  with  geometrical  figures.  In  1785,  however, 
he  renewed  his  chart  of  the  sizes  of  the  European  states, 
and  in  the  year  1786  Plaifair  in  England  came  forward 
simultaneously  with  Randel  and  Remer  in  Germany  with 
a  very  extended  tabular  treatment  of  statistical  data.  Beau- 
fort in  Paris  and  Gaspari  and  Boetticher  in  Germany  in 
1789,  v.  Hoeck  in  1794,  Ehrmann  in  1796,  Ockhart  in 
1804,  and  others  followed  in  the  same  line,  in  part  with 
charts  and  graphic  presentations. 

These  efforts  did  not  meet  with  the  general  approval  of 
the  statisticians.  They  remain,  nevertheless,  an  important 
symptom  of  the  developments  which  were  to  revolutionize 
the  whole  structure  of  statistical  science. 


42  Annals  of  the  American  Academy. 

II.  Institutions  for  National  Statistics  on  a  Scien- 
tific Basis. 

§22.  necessity  for  statistics  during  the  french 
, -        revolution. 

The  necessity  of  resorting  to  statistics  makes  itself  felt 
at  every  essential  change  in  the  form  of  the  state,  just  as 
in  the  transformation  from  the  mediaeval  to  the  modern 
state.  It  proved  to  be  so  much  the  more  indispensable  in 
the  unheard-of  overturning  of  all  existing  conditions  in 
the  French  revolution.  According  to  the  remarkable 
resolutions  of  the  night  of  August  4,  1789,  with  irre- 
pressible enthusiasm,  the  policy  was  accepted  of  creating 
new  forms  based  on  ideas  along  entirely  new  lines.  A  new 
administration,  new  courts,  general  elections,  and  general 
military  service  were  the  principles  to  be  built  up,  on  a 
new  and  geographical  division  of  the  state,  designed  to 
wipe  out  every  remembrance  of  the  historic  ties  which 
bound  the  districts  together.  In  addition,  there  were  new 
means  of  transportation,  a  new  plan  of  custom  duties,  new 
weights  and  measures,  new  money,  but  above  all  the 
project  of  a  new  tax  system,  to  be  founded  chiefly  on  the 
general  income  tax. 

"All  these  projects  were  obliged  to  seek  the  aid  of  sta- 
tistics, and  it  was  found  with  surprise  how  little  material 
was  in  existence  which  could  be  used  for  their  perfection. 

The  National  Assembly  therefore  commissioned  Lavoi- 
sier (born  1743,  executed  1794)  to  collect  as  quickly  as 
possible  the  data  necessary  for  the  preparation  of  the 
reforms  in  administration  and  finance.  He  fulfilled  his 
task  in  an  "  Aperc,u  de  la  richesse  territoriale  et  des  reve- 
nues de  la  France,"  which  he  presented  in  1790.  He  com- 
plains therein  of  the  lack  of  sufficient  material  upon  which 
to  build.  He  estimates  the  population  according  to  the 
ratio   of  one  birth  to  25.75  inhabitants,  which  had  been 


History  of  Statistics.  43 

ascertained  for  other  countries,  though  the  ratio  for  France 
at  least  in  the  present  century  is  1  to  36.8.  His  calcula- 
tions on  the  amount  of  land  under  cultivation  proved  sur- 
prisingly correct,  though  estimated  simply  from  the  num- 
ber and  capacity  of  the  ploughs.  (Statistique  generale  de 
la  France,  Agriculture,  Tome  III.,  1840,  Rapport.) 

These  considerations  tended  to  spread  the  conviction  of 
the  necessity  of  systematically  regulated  returns. 

§  2^.    BUREAUS   FOR  STATISTICS   IN   FRANCE. 

With  considerable   enthusiasm  quite  a  comprehensive 
statistical  activity  was  developed,  and  the  organization  of 
statistical    bureaus   took   place.      The   whole    movement  ■ 
proved,  however,  to  be  merely  temporary. 

Necker  had  established  for  the  statistics  of  finance  and  - 
commerce  a  Bureau  des  renseignements,  which  was  con- 
tinued for  the  publication  of  the  balance  of  trade. 

For  the  general  statistics  of  the  country  it  was  proposed 
to  have  expert  agents  in  every  borough,  and  in  1792  they 
were  required  to  report  certain  facts  to  their  supervisors, 
the  Agents  nationaux.  In  1795  the  minister  Frangois  de 
Neufchateau  established  a  bureau  under  Duquesnoy  for 
the  departmental  statistics  to  be  collected  by  the  Pre- 
fects. The  newly-established  Kataster  Bureau  began  some 
publications  in  1798.  In  1801  Chaptal  commissioned  Jac- 
ques Peuchet  to  give  a  description  of  a  department  to  serve 
as  a  model,  and  organized  a  Bureau  de  statistique  under 
Coquebert  de  Montbret  for  the  purpose  of  securing  statis- 
tics of  the  departments  on  this  plan.  The  descriptions 
were  completed  for  only  53  departments  and  were  discon- 
tinued in  18 1 5.  Nevertheless,  with  the  assistance  of  the 
cooperators  in  these  works,  there  appeared,  in  1 803,  Her- 
bin's  °  Statistique  generale  et  particuliaire  de  la  France  et 
de  ses  colonies  avec  une  description  topographique,  agri- 
cole,  politique,  industrielle  et  commerciale  de  cet  etat." 

In  1804  appeared  the  "  Dictionnaire  universel  geograph- 


44  Annals  of  the  American  Academy. 

ique,  statistique,  historique  et  politique  de  la  France," 
which  had  been  ordered  in  1790  by  the  National  Assem- 
bly, and  meritoriously  completed  by  Prudhomme. 

In  1804  the  official  work,  Statistique  generate  de  la 
France  publiee  par  ordre  de  M.  l'Empereur  et  Roi  et 
redigee  sur  les  memoires,  adresses  au  Ministere  de  l'lnte- 
rieur  par  MM.  les  prefets,  was  successfully  brought  to 
completion. 

Very  few  data  of  these  works  rest  upon  actual  enumera- 
tion. Even  the  census  of  the  population,  which  had  been 
attempted  in  1801  and  again  in  1805  had  each  time  been 
successful  only  in  the  departments  and  the  results  varied 
greatly.  An  actual  enumeration  in  Paris  was  accomplished 
for  the  first  time  in  18 17,  according  to  the  plans  of  J.  B. 
de  Fourier.  The  estimates  of  experts  furnished  the  largest 
portion  of  the  material.  Great  errors  were  therefore  pos- 
sible. It  required,  however,  by  this  method  very  little 
effort  to  broaden  the  sphere  of  the  questions,  and  even 
secure  estimates  concerning  things  about  which  the  per- 
sons interested  would  be  disinclined  to  furnish  information. 
The  predominance  of  this  form  of  official  inquiry,  which 
we  call  the  enquete,  is  characteristic  for  French  statistics 
down  to  the  present  day. 

That  under  the  circumstances  statistics  attracted  general 
interest  and  became  the  fashion,  is  easily  comprehended. 
In  1803,  under  the  protection  of  Cambaceres,  a  Societe  de 
Statistique  was  founded  at  Paris.  Donnant  and  Peuchet 
published  in  1805  text-books,  in  Achenwall's  style,  of 
Statistique  elementaire;  in  1802-1804  Ballois  edited  An- 
nates de  Statistique ;  Deferriere,  the  chief  of  the  statistical 
bureau,  published  in  1 803-1 804  Archives  statistiques  de  la 
France.  The  "  Moniteur  universel,"  founded  in  1789,  as 
well  as  the  "Journal  des  Mines,"  appearing  since  1792, 
contained  numerous  statistical  essays. 

The  empire,  however,  brought  an  end  to  all  these  efforts. 
Although  Napoleon  had  said  "  La  statistique  est  le  budget 
'des  choses  et  sans  budget  point  de  salut  public,"  he  dis- 


History  of  Statistics.  45 

solved  in  1806  the  Commissions  and  the  Societe  de  Statis- 
tique,  and  prohibited  all  publications  with  the  exception  of 
four  Exposees  de  la  situation  de  l'Empire,  which  were  pre- 
pared by  the  Minister  of  the  Interior,  Count  Montalivet, 
in  1809,  181 1,  1 8 13,  and  again  in  18 15  during  the  hundred 
days. 

§  24.   STATISTICAL    BUREAUS    IN    ITALY,   SPAIN,   WESTPHALIA, 
AND   BAVARIA. 

As  a  result  of  the  increased   interest   in   statistics  in    j 

France,  and  in  part  at  the  orders  of  the  French  adminis- 

j  tration,  some  of  the  neighboring  countries  created  statisti- 

'  cal  bureaus.    They  were,  as  a  rule,  short-lived.    The  Italian 

I  Republic  received   one  in    1803,  which,  placed  under  the 

.-  direction  of  Gioja,  continued  in  existence  until  1809.     In 

Spain,  during  the  French  rule,  a  Departamento  del  fomento 

general  del  Reino  was  established.     For  Westphalia  there 

was  a  statistical  bureau  under  Hassel,  in  1809,  which  did 

not  survive  the  fall  of  the  kingdom. 

In  Bavaria,  General  Raglowich  attempted,  in  180 1,  to 
found  a  military  statistical  bureau,  which,  however,  did 
not  last  long.  Later,  an  ordinance  of  December  12,  1806, 
provided  for  a  regular  report  of  lists  of  all  births,  mar- 
riages, and  deaths  in  the  new  kingdom,  and  further  ordi- 
nances of  July  17,  1808,  and  September  27,  1809,  directed 
the  provincial  authorities  to  send  in  annual  reports  of  ad- 
ministration, and  to  combine  with  them  the  material  for  as 
complete  statistics  of  the  kingdom  as  possible.  Returns 
were  required  especially  concerning  dwellings,  number 
and  movement  of  the  population,  immigration  and  emi-  « 
gration,  mining,  agriculture,  trades,  laborers  and  products, 
commerce,  prices,  institutions  of  credit,  care  of  the  poor, 
sanitary  conditions,  medical  arrangements,  and  schools. 
As  it  was  soon  perceived  that  returns  upon  so  various  sub- 
jects could  not  be  compared  and  were  of  little  value  unless  • 
made  according  to  uniform  schedules,  ordinances  of  18 10 


46  Annals  of  the  American  Academy. 

and  1812  provided  special  tables  for  the  arrangement  of  the 
data.  The  returns  for  1809-10  and  1811-12  embraced, 
nevertheless,  438  volumes  in  folio,  and  the  bureau  for 
topography  and  statistics,  established  in  18 1 3,  held  the 
continuation  and  preparation  of  this  material  to  be  im- 
practicable. 

§  25.   FOUNDATION    OF    THE    PRUSSIAN   STATISTICAL   BUREAU. 

Much  greater  was  the  influence  of  the  reorganization  of 
\  the  official  statistics  of  Prussia.  It  was  brought  about  in 
1805  by  Minister  v.  Stein  on  the  proposal  of  Leopold 
Krug. 

Krug  (born  1770,  died  1843)  nac*  written  several  statis- 
tical and  economic  works  while  still  in  subordinate  official 
position  in  Halle.  At  his  request,  in  1799,  he  was  admitted 
into  the  Prussian  service  as  registrar  in  the  "  Lehn  "  depart- 
ment, with  permission  to  make  use  of  the  secret  registers 
of  the  departments  in  which,  as  in  the  time  of  Frederick 
the  Great,  statistical  material  was  collected.  Upon  these 
foundations  he  prepared,  in  1805,  his  Betrachtungen  iiber 
den  National- Reichtum  des  preussischen  Staates.  The  two 
moderate-sized  volumes  contain  his  calculations  on  the 
Physiocratic  basis  of  the  gross  national  income  from  the 
returns  of  agriculture  and  the  excess  in  foreign  trade. 
From  these  he  attempts  to  ascertain  the  net  income  of  the 
nation  after  exclusion  of  the  income  which  simply  passes 
from  hand  to  hand,  by  subtracting  the  entire  consumption 
of  home  raw  products  and  imported  foreign  products  and 
manufactures.  The  method  is  obviously  open  to  objection, 
but  as  a  most  careful  turning  to  account  of  statistical  data 
the  book  has  great  merits. 

A  Cabinet  order  of  May  28,  1805,  gave  Minister  v. 
Stein  directions  to  establish  a  bureau  for  the  continuation 
and  correction  of  these  data  annually.  In  it  the  statistical 
material  collected  in  the  various  departments  could  be 
united  and  formed  into  a  systematized  whole. 


History  of  Statistics.  47 

The  bureau  was  established  immediately  with  the  Min- 
ister as  chief.  Krug  was  the  only  official,  though  Beguelin 
and  others  rendered  assistance.  Soon  after,  on  May  22, 
1806,  the  first  annual  report  was  ready.  It  comprehended 
24  tables  of  varied  contents  on  population,  topography, 
agriculture,  manufactures  and  commerce,  transportation, 
excise,  consumption,  morality,  and  culture.  Returns  of 
churches  and  municipalities,  of  postal  and  tax  administra- 
tion, were  lacking. 

Upon  the  remonstrance  of  various  bureaus  and  their 
demand  that  their  communications  should  be  kept  secret, 
a  Cabinet  order  of  October  16,  1806,  the  second  day  after 
the  battle  of  Jena,  ordered  that  the  publication  of  returns 
on  population,  production,  manufactures,  culture,  com- 
merce, shipping,  and  civil  status  should  be  permitted,  but 
that  the  returns  of  private  property,  of  moneyed  institutions, 
credit  systems,  state  debts,  and  public  revenues  (Boeckh, 
p.  28.     See  §  1 1)  should  not  be  published. 

§  26.    REESTABLISH MENT   OF   THE   PRUSSIAN   STATISTICAL 
BUREAU. 

As  soon  as  the  peace  of  Tilsit  permitted  the  regulation 
of  the  state  affairs,  an  administrative  order  of  the  govern- 
ment of  December  26,  1808,  confirmed  the  previous  regu- 
lations as  to  the  statistical  returns.  Yet  the  necessary 
economy  in  the  official  service  and  the  examination  of 
Krug's  plan  by  the  "  Oberprasidien  "  led  to  some  restric- 
tion of  its  scope.  * 

Joh.  Gottfr.  Hoffmann  (born  1765,  died  1847.  At  this 
time  "  Bauass^ssor,"  later  Ministerialrath  fur  Gewerbe 
*  Polizei,  and  professor)  contended  that  only  those  questions 
should  be  asked  to  which  it  seemed  reasonable  to  expect 
correct  answers.  He  reduced  Krug's  questions  to  less 
than  one-third,  but  drew  within  their  scope  all  suitable 
material  which  could  be  gathered  together  from  the  affairs 
of  the  public  offices.     On  account  of  these  reasonable  pro- 


48  Annals  of  the  American  Academy. 

posals  a  Cabinet  order  of  October  4,  18 10,  appointed  him. 
Director  of  the  statistical  bureau,  with  Krug  and  the 
topographer  Engelhardt  as  associates. 

His  own  principles,  as  well  as  the  state  of  the  finances, 
led  Hoffmann  to  exercise  the  greatest  caution,  so  as  to 
burden  as  little  as  possible  the  officials  who  made  the 
returns.  What  he  brought  together,  however,  was  the 
result  of  an  actual  ascertainment  of  the  facts.  He  preferred 
to  abandon  altogether  the  attempt  to  secure  returns  on  agri- 
culture, causes  of  death,  churches,  schools,  and  sanitary 
conditions  than  to  content  himself  with  unreliable  data. 
%  His  principle  was  a  direct  enumeration  in  everything.  In 
this  conception  of  the  method  he  stood  in  an  essentially 
contradictory  position  to  that  of  the  French  statistics,  and 
though  enumeration  and  enquete  are  certainly  to  be  justi- 
fied or  rejected  according  to  the  specific  objects  and  pur- 
poses for  which  they  are  to  be  used,  the  enquete  has  never 
won  for  itself  a  prominent  place  in  Prussian  or  in  German 
statistics  generally.  The  German  statistics  have  not  en- 
couraged multiplicity  in  the  returns,  where  it  could  not 
be  obtained  by  additional  enumerations,  or  by  distinctions 
introduced  into  the  enumeration,  or  by  a  combination  of 
results  obtained  by  direct  enumeration. 

Hoffmann's  work  rests,  therefore,  on  an  uncommonly 
limited  basis  of  materials,  but  he  understood  how  to  use 
them  with  surprising  versatility  and  productive  power, 
and  to  supply  the  deficiencies  from  the  rich  treasure  of 
his  scientific  acquirements  and  experience.  (Boeckh,  §  44. 
See  §  11.) 

HI.  Limitation   of   the  Field  of  Statistical   Science. 
§27.  limitation  of  achenwall's  statistics. 

The  appearance  of  the  official  statistics  in  such  vigor  in 
France  and  Prussia  was  combined  with  a  decisive  revolu- 
tion in  the  whole  field  of  scientific  statistics. 


History  of  Statistics.  49 

Although  statistical  bureaus  were  organized  only  grad- 
ually in  other  states,  yet  the  necessity  was  generally  felt  of 
I  studying  the  state  of  the  nation  from  the  current  affairs  of 
J  its  administrative  offices,  ,as  well  as  from  special  returns  at 
stated  intervals. 

This  attention  to  the  internal  affairs  of  the  nation  con- 
tained in  itself  a  certain  antithesis  to  Achenwall's  general 
descriptive  comparisons  of  all  nations.  It  soon  appeared 
from  the  interdependence  of  the  results  that  the  statistics 
of  Achenwall,  of  Busching,  and  of  Siissmilch,  were  merely 
parts  of  the  same  sphere  of  ideas.  This  was  first  recog- 
nized theoretically  by  Niemann  in  his  "  Abriss  der  Sta- 
tistik  oder  Staatenkunde "  (1804)  1807.  (John,  p.  119. 
See  §  7.) 

Even  before  the  death  of  v.  Schlozer  it  was  felt  that  the 
fundamental  ideas  of  Achenwall's  statistics  were  shaken* 
by  the  ever-increasing  stream  of  official  statistics  and  by 
the  numerical  treatment  which  was  based  on  them.  Tabu- 
lar and  graphic  presentations  and  comparisons  came  more 
and  more  in  vogue  through  the  efforts  of  v.  Brunn,  Don- 
nant,  Lichtenstern,  v.  Schmidtberg,  and  especially  Hassel 
(Grundriss  der  Statistik,  1805,  1809,  1825).  But  v.  Schlozer 
with  Luder,  Rehberg,  Brandis,  Heeren,  considered  this  as 
an  aberration  (Luder,  Geschichte  der  Statistik,  p.  214; 
Kritik  der  Statistik,  §  14).  In  1806  and  1807  a  passionate 
controversy  arose  against  the  brainless  bungling  of  the 
number  statisticians,  the  slaves  of  the  tables,  the  skeleton- 
makers  of  statistics.  Undoubtedly  the  pupils  of  Achen-  I 
wall  were  right  that  statistics  cannot  evade  the  considera-  ; 
tion  of  the  highest  problems  of  political  life.  But  they  i 
deceived  themselves  as  to  the  manner  in  which  this  ideal, 
purpose  of  statistics  was  to  be  attained.  They  underesti- 
mated the  significance  of  the  material  prepared  for  com- 
parison according  to  number  and  measure,  the  indispensa- 
ble premise  of  every  critically  correct  conclusion  from 
statistics.  The  opponents  in  the  sharp  attack  were  them- 
4 


50  Annals  of  the  American  Academy. 

selves,  however,  not  sufficiently  clear  how  new  and  precise 
limits  for  their  science  should  be  determined. 


§  28.    ELIMINATION   OF   POLITICAL   ECONOMY,    OF   PUBLIC   AND 
ADMINISTRATIVE   LAW. 

In  this  state  of  affairs  the  decisive  factor  in  the  develop- 
ment of  statistical  theory  was  the  specialization  of  the 
various  fields  of  knowledge  which  at  the  beginning  of  the 
century  accompanied  the  increased  intellectual  activity  and 
the  unusual  extension  of  the  field  of  investigation  and 
research. 

Adam  Smith,  in  his  "  Inquiry  into  the  Nature  and  Causes 
of  the  Wealth  of  Nations,"  1776,  furnished  a  firm  footing 
for  the  science  of  political  economy  by  his  clear  definition, 
system,  and  method.  With  the  beginning  of  the  century 
political  economy  began  to  appear  as  an  independent  sub- 
ject with  special  professors  in  the  lectures  and  studies  of 
the  German  universities,  as  well  as  in  England  and  France. 
Thus  the  connection  with  other  political  sciences,  and 
hence  with  statistics  was  dissolved. 

In  England,  Stewart  (1799),  Malthus  (1804),  Ricardo 
(18 1 2),  McCulloch  (1825),  and  others  represented  the  new 
science;  in  France,  Say  (1803),  Sismondi  (18 19),  and  Droz 
(1828).  In  Germany  there  were  besides  Garve,  who  trans- 
lated Smith,  Sartorious  (1796),  Jacob  (1805),  Kraus  (died 
1807),  Hufeland  (1807),  Liider  (1820),  Rau  (182 1),  Politz 
(1823),  and  v.  Rotteck  (1829),  all  of  whom  lectured  on 
1  political  economy  in  Smith's  manner  as  a  discipline,  which 
included  all  that  related  to  economic  policy,  which  the 


i. 


'■older  school  of  Achenwall  and  indeed  v.  Schlozer  held 
to  be  a  field  of  statistics. 

Similarly  the  closely  connected  subjects  of  public  and 
administrative  law  severed  their  connection  with  statistics. 
There  had  been  before  this  time  separate  chairs  for  these 
subjects  in  the  universities,  but  at  this  time  the  separation 
became  general  and  permanent. 


History  of  Statistics.  51 

The  philosophical  consideration  of  state  and  law  by- 
Kant  (1796),  Fichte  (1796),  and  Hegel  (1821),  as  well  as 
the  historical  conception  for  which  Justus  Moser  (1765)  had 
given  the  stimulus,  and  which  Schlosser  (1777),  Putter 
(1786),  and  Eichhorn  (1808)  had  moulded,  gave  new  points 
of  departure,  and  none  of  the  works  of  Welker  (18 13), 
Haller  (1816),  Kluber  (1818),  Sal.  Zachariae  (1820),  P61itz 
(1823),  and  Heffter  (1829),  hold  fast  to  the  traditional  con- 
nection with  Achenwall's  statistics. 

§  29.    ELIMINATION   OF   THE   GEOGRAPHICAL   ELEMENT. 

The  geographical  notions  which  Seb.  Miinster  and  Pierre 
d'Avity  and  even  Busching  had  incorporated  with  statis- 
tics, showed  themselves  more  and  more  to  be  a  special 
branch  of  science. 

Gatterer  had  endeavored  in  1775  to  lead  geography 
away  from  the  political  and  statistical  basis,  by  giving 
prominence  rather  to  the  natural  differences  of  the  surface 
of  the  earth  and  the  conditions  which  they  impose  on  civ- 
ilization.    Zeune's  "  Gaea,"  1808,  had  the  same  tendency. 

Decisive  in  the  matter,  however,  was  the  distinguished 
example  of  C.  Ritter  (born  1779,  died  1859)  in  n^s  volumi- 
nous "  Erdkunde  im  Verhaltniss  zur  Natur  und  Geschichte 
des  Menschen  oder  allgemeine  vergleichende  Geographic" 
He  places  the  reader  in  the  position  of  the  traveller,  he  ap- 
peals to  the  eye  and  heart,  and  gives  exact  information  of 
events  and  experiences.  The  gaps  in  the  material  he  does 
not  attempt  to  conceal,  but  endeavors  to  place  the  reader 
in  a  position  to  supply  them,  as  well  as  may  be,  by  the 
analogies  which  his  own  judgment  suggests.  The  result, 
therefore,  is  a  difference  in  the  principles  of  geographical 
and  statistical  observation.  From  the  totality  of  the 
phenomena,  geography  judges  from  its  standpoint  as  to 
what  is  unseen,  and  assumes  by  induction  that  what  is 
typical  may  be  found  there.  Statistics  searches  its  entire 
field  for  distinct  units,  none  of  which  may  escape  observa- 


52  Annals  of  the  American  Academy. 

tion,  but  cannot  draw  into  consideration  any  other  phe- 
nomena. The  results  are  for  both  mutually  useful,  but  the 
methods  by  which  they  are  obtained  so  totally  different 
that  the  geographer  is  not  as  such  a  statistician,  nor  is  the 
statistician  as  such  a  geographer. 

§  30.  separation  of  practical  life  insurance  from 

STATISTICS. 

*  In  the  field  of  life  insurance  a  complete  separation  from 
the  statistics  of  population  occurred,  which  continues  up 
to  the  present  day. 

Life  insurance  assumed  such  dimensions  that  at  the  end 
of  the  century  there  were  more  than  ten  large  institutions 
in  England.  Others  were  established  in  1806  at  Hamburg, 
1 8 19  at  Paris,  1824  in  Belgium,  1826  in  Italy,  1828  at 
Lubeck,  1829  at  Gotha,  1830  at  New  York,  1835  in 
Russia. 

Of  a  similar  nature  were  the  widows'  treasuries,  which, 
in  part  at  least,  had  been  founded  on  earlier  institutions, 
among  them  the  Prussian  treasury  for  the  widows  of  offi- 
cials, founded  in  1776. 

The  failure  of  several  inadequately  equipped  institutions 
in  England,  the  investigation  of  the  Caisse  Lafarge  in 
1809  at  Paris,  and  the  discovery  in  1836  of  the  swindle 
of  the  bubble  companies  did  not  interrupt  this  develop- 
ment. 

Laplace,  Baily,  Lacroix,  and  Littrow  advanced  the  neces- 
sary mathematical  calculations.  The  more  critically  the 
basis  of  life  insurance  was  examined  the  more  evident  it 
became  that  the  order  of  mortality  did  not  furnish  a  suffi- 
cient basis  of  calculation  for  the  expectation  of  life  among 
the  persons  of  various  ages  and  occupations  who  were 
seeking  insurance.  The  attempt  was,  therefore,  made  to 
gain  a  scale  for  the  tariffs  from  the  growing  material  of 
the  companies  themselves.  Milne  prepared,  about  18 15, 
the  Carlisle  table  on  the  basis  of  observations  in  Carlisle 


History  of  Statistics.  53 

from  1779-87;  Finlaison,  in  1829,  the  Government  Tables 
from  the  tontines  and  annuities;  Morgan,  1834,  the  Equi- 
table experience  table,  from  the  experiences  of  that  com- 
pany between  1762  and  1829;  and,  finally,  Brune  prepared 
from  the  records  of  the  Preussischen  Allgemeinen  Witt- 
wenverpflegungs-Anstalt,  from  1776  to  1834,  a  death  table 
of  great  value  for  the  widows'  treasuries.  While  the  gen- 
eral calculations  of  mortality  did  not  lose  their  value  as  a 
measure  of  the  welfare  of  the  population,  the  close  con- 
nection between  life  insurance  and  Sussmilch's  statistics 
ceased  to  exist. 

§31.    DECLINE   OF  STATISTICS   AS   A   SYSTEM. 

The  development  of  the  new  scientific  studies,  with  their 
much  more  profound  treatment,  deprived  Achenwall's  Sta- 
tistics of  essential  parts  of  its  subject-matter.  The  data 
of  the  traditional  system  of  "  Staatsmerkwiirdigkeiten" 
assumed  unavoidably  a  superficial  character,  and  statistics 
as  a  university  study  sank  into  insignificance.  It  is  true 
Luder  (died  18 19)  in  Jena,  Meusel  (died  1820)  in  Erlangen, 
Niemann  (died  1832)  in  Kiel,  Mannert  (died  1834)  in 
Munich,  and  Heeren  (died  1842)  in  Gottingen,  still  taught 
statistics  with  success  according  to  v.  Schlozer's  ideas.  In 
Austria  v.  Holzgethan,  Schnabel,  v.  Schlieben,  Franzl,  and 
others  were  able  to  keep  the  traditions  of  the  school  alive, 
as  statistics  so  understood  still  formed  a  part  of  the  re- 
quirements in  the  examinations  for  position  in  the  official 
service. 

But  the  old  teaching  died  out  with  the  teachers.  Tabu- 
lar statistics  in  their  then  condition  could  not  be  taught 
j  from  the  professorial  chair.  Luder,  although  he  recog- 
nized the  merits  of  Sussmilch's  statistics,  felt  the  change 
so  strongly  that  he  doubted  the  possibility  of  scientific 
statistics  (Luder,  Kritik  der  Statistik  und  Politik,  1 8 12, 

§  57). 


52  Annals  of  the  American  Academy. 

tion,  but  cannot  draw  into  consideration  any  other  phe- 
nomena. The  results  are  for  both  mutually  useful,  but  the 
methods  by  which  they  are  obtained  so  totally  different 
that  the  geographer  is  not  as  such  a  statistician,  nor  is  the 
statistician  as  such  a  geographer. 

§  30.  separation  of  practical  life  insurance  from 
statistics. 

-,  In  the  field  of  life  insurance  a  complete  separation  from 
/  the  statistics  of  population  occurred,  which  continues  up 
to  the  present  day. 

Life  insurance  assumed  such  dimensions  that  at  the  end 
of  the  century  there  were  more  than  ten  large  institutions 
in  England.  Others  were  established  in  1806  at  Hamburg, 
1 8 19  at  Paris,  1824  in  Belgium,  1826  in  Italy,  1828  at 
Liibeck,  1829  at  Gotha,  18 30  at  New  York,  1835  in 
Russia. 

Of  a  similar  nature  were  the  widows'  treasuries,  which, 
in  part  at  least,  had  been  founded  on  earlier  institutions, 
among  them  the  Prussian  treasury  for  the  widows  of  offi- 
cials, founded  in  1776. 

The  failure  of  several  inadequately  equipped  institutions 
in  England,  the  investigation  of  the  Caisse  Lafarge  in 
1809  at  Paris,  and  the  discovery  in  1836  of  the  swindle 
of  the  bubble  companies  did  not  interrupt  this  develop- 
ment. 

Laplace,  Baily,  Lacroix,  and  Littrow  advanced  the  neces- 
sary mathematical  calculations.  The  more  critically  the 
basis  of  life  insurance  was  examined  the  more  evident  it 
became  that  the  order  of  mortality  did  not  furnish  a  suffi- 
cient basis  of  calculation  for  the  expectation  of  life  among 
the  persons  of  various  ages  and  occupations  who  were 
seeking  insurance.  The  attempt  was,  therefore,  made  to 
gain  a  scale  for  the  tariffs  from  the  growing  material  of 
the  companies  themselves.  Milne  prepared,  about  18 15, 
the  Carlisle  table  on  the  basis  of  observations  in  Carlisle 


History  of  Statistics.  53 

from  1779-87;  Finlaison,  in  1829,  the  Government  Tables 
from  the  tontines  and  annuities ;  Morgan,  1834,  the  Equi- 
table experience  table,  from  the  experiences  of  that  com- 
pany between  1762  and  1829;  and,  finally,  Brune  prepared 
from  the  records  of  the  Preussischen  Allgemeinen  Witt- 
wenverpflegungs-Anstalt,  from  1776  to  1834,  a  death  table 
of  great  value  for  the  widows'  treasuries.  While  the  gen- 
eral calculations  of  mortality  did  not  lose  their  value  as  a 
measure  of  the  welfare  of  the  population,  the  close  con- 
nection between  life  insurance  and  Sussmilch's  statistics 
ceased  to  exist. 

§31.    DECLINE   OF  STATISTICS   AS   A   SYSTEM. 

The  development  of  the  new  scientific  studies,  with  their 
much  more  profound  treatment,  deprived  Achenwall's  Sta- 
tistics of  essential  parts  of  its  subject-matter.  The  data 
of  the  traditional  system  of  "  Staatsmerkwiirdigkeiten" 
assumed  unavoidably  a  superficial  character,  and  statistics 
as  a  university  study  sank  into  insignificance.  It  is  true 
Liider  (died  18 19)  in  Jena,  Meusel  (died  1820)  in  Erlangen, 
Niemann  (died  1832)  in  Kiel,  Mannert  (died  1834)  in 
Munich,  and  Heeren  (died  1842)  in  Gottingen,  still  taught 
statistics  with  success  according  to  v.  Schlozer's  ideas.  In 
Austria  v.  Holzgethan,  Schnabel,  v.  Schlieben,  Franzl,  and 
others  were  able  to  keep  the  traditions  of  the  school  alive, 
as  statistics  so  understood  still  formed  a  part  of  the  re- 
quirements in  the  examinations  for  position  in  the  official 
service. 
\  But  the  old  teaching  died  out  with  the  teachers.  Tabu- 
i  lar  statistics  in  their  then  condition  could  not  be  taught 
I  from  the  professorial  chair.  Liider,  although  he  recog- 
nized the  merits  of  Sussmilch's  statistics,  felt  the  change 
so  strongly  that  he  doubted  the  possibility  of  scientific 
statistics  (Liider,  Kritik  der  Statistik  und  Politik,  1 8 12, 
§57)- 


/ 


54  Annals  of  the  American  Academy. 

§  32.  state  of  official  statistics. 

To  supply  this  deficiency  seems  to  have  been  in  a  cer- 
tain sense  part  of  the  idea  which  led  to  the  foundation  of 
the  statistical  bureaus.  Originally  topographical — statisti- 
cal descriptions  of  the  land,  the  character  of  its  soil,  its 
national  and  political  relations,  and  economic  conditions 
were  required  from  them. 

It  soon  became  evident  that  the  answers  even  to  the  sim- 
plest questions  of  population  and  industrial  statistics, 
which,  were  indispensable  to  the  government,  gave  rise 
to  a  mass  of  material  which  could  hardly  be  handled.  It 
was  found  that  often  the  most  desirable  information  could 
by  no  means  always  be  obtained  from  the  current  affairs 
of  the  offices,  but  required  special  investigations  and 
returns. 

The  officers  were  bound  by  the  bureaucratic  rules  of  the 
service.  Problems  with  distinct  objects  in  view,  and  in- 
volving responsibility  in  their  decision,  were  sent  to  them, 
cases  where  the  solution  could  have  the  necessary  cer- 
tainty only  by  a  wholly  impartial,  well-considered,  and 
unerring  investigation.  The  demands  extended  generally 
to  all  the  details,  to  the  differences  between  various  dis- 
tricts, industrial  classes,  or  local  institutions,  so  that  the 
greatest  specialization  was  necessary. 

For  this  imperative  labor  neither  the  officials  nor  the 
assistants,  generally  only  temporarily  employed,  nor  least 
of  all  the  appropriations  for  these  subordinate  functions, 
were  sufficient. 

The  activity  of  the  bureaus  became,  therefore,  on  the  one 
hand,  more  intense ;  on  the  other,  more  restricted.  The 
concentration  of  all  statistics  in  one  bureau  could  not  yet 
be  thought  of,  and  neither  the  same  principles  nor  treat- 
ment governed  the  "ressort"  arrangements  in  the  different 
states.  Though  uniformity  appeared  later,  yet  until  the 
middle  of  the  century  the  organization  and  the  enterprises 


History  of  Statistics.  55 

of  official  statistics  retained  an  individual  character,  which 
makes  them  interesting  on  account  of  their  many  specific 
peculiarities. 


IV.  Rise  of  National  Statistics  in  the  Various 
Civilized  Nations. 

§  33.   FRANCE. 

The  Restoration  was  by  no  means  more  favorably  in- 
clined toward  statistics  than  the  Empire  (§  23).  The  pub- 
lications were  very  meagre. 

From  18 1 5  appeared  a  yearly  "Tableau  general  du 
commerce  de  la  France,"  with  returns  on  the  coasting 
trade,  published  by  the  administration  of  customs.  In 
addition  there  appeared  from  18 13  reports  on  recrutement 
(1830  by  Petigny),  and  from  1820  by  the  Marine  Ministry 
"Notices  sur  les  colonies  franchises,"  and  also  "  Comptes 
rendus  des  travaux  des  ingenieurs  des  mines." 

In  1821,-1829  Count  Chabral,  Prefect  of  the  Seine,  pub- 
lished comprehensive  statistics  of  Paris,  prepared  by  Vil- 
lot,  and  1825  and  1833  Guerry  de  Champneuf  prepared 
reports  on  the  administration  of  criminal  justice. 

In  1827  a  Societe  de  statistique  was  founded  with  official 
permission  at  Marseilles.  At  Paris  the  Societe  francaise 
de  statistique  universelle  was  permitted  to  organize  in 
1829.  It  was  not  till  after  the  July  revolution  of  1832 
that  the  Institut  de  France  was  allowed  to  reestablish  the 
Academie  des  sciences  morales  et  politiques,  which  had 
been  suppressed  during  the  Consulate.  It  contained  a 
section  for  Economie  politique  et  statistique. 

In  1833  Thiers  announced  his  intention  to  the  Chambers 
of  repeating  the  Statistique  generale  de  la  France  on  a 
new  plan.  He  founded  under  Moreau  de  Jonnes  a  Bureau 
de  la  statistique. 

This  bureau  published,  1835,  Tom.  I.  Finances;  1837, 
Tom.  II.  Territoire  et  population;    1838,  Tom.  X.  Com- 


56  Annals  of  the  American  Academy. 

merce  exterieur;  1840  and  1841,  Tom.  III.-VI.  Agricul- 
ture (the  results  of  the  agricultural  enquete  of  1839-42); 
1843  and  1844,  Tom.  XL,  XII.  notices  from  the  general 
administration  (Bienfaisance,  Etablissements  de  repres- 
sion); finally,  1847-52,  Tom.  VII.  and  VIII.,  Industrie 
manufacturiere  et  arts  et  metiers,  the  results  of  an  in- 
dustrial enquete  begun  in  1839  and  taken  up  again  in  1845. 

Besides  the  above  there  were  the  publications  of  the 
administration  of  customs,  of  the  Ministries  of  finance,  of 
agriculture,  and  of  commerce. 

The  events  of  the  year  1848  led  to  a  new  enquete  on 
rural  and  industrial  labor.  It  was  completed  only  in  Paris 
by  the  Chamber  of  Commerce,  and  the  results  published 
in  the  valuable  work,  Statistique  de  l'industrie  a  Paris. 
On  January  1,  185 1,  2941  statistical  cantonal  and  district 
commissions  were  organized  for  carrying  through  the 
agricultural  enquete  of  1852.  The  commissions  super- 
vised the  returns  to  500  questions  in  every  canton. 

In  i860,  on  the  occasion  of  the  treaty  of  commerce  with 
England,  a  new  and  comprehensive  enquete  was  under- 
taken by  the  Conseil  superieur  de  l'agriculture,  du  com- 
merce et  de  l'industrie,  of  which  "Agriculture"  appeared 
in  1 86 1.  The  enquete  of  Parisian  industry  was  repeated 
in  i860  (Statistique  de  l'industrie  a  Paris,  1864). 

In  1866  it  was  deemed  important  to  demonstrate  the 
influence  of  the  treaty  of  commerce  of  i860  on  French 
agriculture.  An  enquete,  concluded  in  May,  1870,  was, 
therefore,  undertaken  under  a  special  commission,  whose 
labors,  Enquete  agricole,  ministere  de  l'agriculture,  1869- 
70,  fill  36  volumes. 

In  1879  a  new  agricultural  enquete  was  assigned  offi- 
cially to  the  Societe  nationale  d'agriculture  de  France,  the 
results  appearing  in  2  volumes,  1880,  "Enquete  sur  la 
situation  de  l'agriculture  en  1879,"  by  Barral. 


History  of  Statistics.  57 

§  34.  prussia  and  the  other  german  states. 

The  official  statistics  of  all  German  states  assumed  in 
contents  and  character  great  uniformity  from  the  example 
of  Prussia,  and  in  consequence  of  the  gradual  development 
of  common  custom  and  tax  systems.  The  organization  of 
the  bureaus  and  the  mode  of  publication  remained  very 
divergent. 

In  Prussia  the  statistical  bureau  continued  without  changes 
to  be  the  centre  of  the  system  (§  25).  Under  Hoffmann, 
who  surrendered  the  place  in  1844  to  Dieterici,  and  died 
in  1847,  no  regular  publications  were  made.  Hoffmann 
wrote  essays  in  the  "  Staats-Anzeiger  "  and  in  the  reports 
of  the  Academy.  His  first  more  extensive  work  was  "  Die 
Bevolkerung  des  preussischen  Staates  nach  den  Ergebnis- 
sen  der  1837  aufgenommenen  Nachrichten " ;  in  1838  ap- 
peared "  Die  Lehre  vom  Gelde";  1840,  "Die  Lehre  von 
den  Steuern";  1843,  *'  Bevolkerungs-  Geburts- Ehe- und 
Sterblichkeits-verhaltnisse  im  Preussischen  Staate."  In  the 
same  period  Ferber  published, beginning  in  1829,  regularly 
his  "  Beitrage  zur  Kenntniss  des  gewerblichen  und  kom- 
merziellen  Zustandes  des  Preussischen  Staates  "  from  the 
papers  of  the  ministry  of  finance.  These  were  continued 
by  Dieterici  as  "  Uebersichten  von  Verkehr  und  Verbrauch 
im  Preussischen  Staate  und  Zollverein  "  in  1838,  and  from 
the  following  year  by  the  "  Centralblatt  der  Abgaben, 
Gewerbe-  und  Handels-Gesetzgebung  und  Verwaltung." 
Dieterici  (born  1790,  died  1859)  published,  1846,  the  work 
"  Der  Volkswohlstand  des  Preussischen  Staates,"  which 
compares  the  state  of  things  in  1806,  1830,  and  1845  '■>  anc* 
began  after  the  census  of  1845  with  the  "  Statistische  Ta- 
bellen  des  Preussischen  Staates"  the  periodical  publica- 
tions of  the  bureau,  for  whose  extension  into  all  the  details 
of  the  materials  the  new  legislature  of  the  country  in  1850 
had  provided  the  means.  From  i860  to  1882  the  bureau 
was  in  charge  of  Ernst  Engel  (born  1821).  In  1861  a 
central  statistical  commission  was  appointed. 


58  Annals  of  the  American  Academy. 

In  Bavaria  (§  24)  the  statistical-topographical  bureau, 
established  in  1813,  transferred  the  preparation  of  special 
topographical  charts  to  the  Ministry  of  War.  In  the  year 
1 8 18  the  yearly  reports  were  limited  to  a  few  returns,  and 
after  1825  the  reports  were  issued  triennially.  In  1833  and 
1839  new  ordinances  wrought  a  change.  With  the  last 
v.  Hermann  (born  1795,  died  1868)  began  his  work  as 
Director.  In  1850  he  founded  the  "  Beitrage  zur  Statistik 
des  Konigreiches  Bayern." 

Hannover  made  plans  in  183 1  for  the  regular  preparation 
of  the  statistical  material  of  the  various  branches  of  the 
administration.  However,  it  was  not  till  1848  that  the 
plan  was  carried  into  execution,  with  the  organization  of  a 
statistical  bureau.  It  published  from  1850  "Zur  Statistik 
des  Konigreiches  Hannover." 

In  Saxony  the  first  impulse  was  given  by  the  Statistische 
Vereine  fur  das  Konigreich  Sachsen,  which  were  founded 
in  1837  by  v.  Schlieben.  The  cooperation  of  the  govern- 
ment enabled  them  to  publish,  up  to  1849,  18  parts  of  their 
"  Mittheilungen."  This  very  honorable  private  work  was 
transferred  in  1850  to  the  Ministry  of  the  Interior,  which 
founded  a  statistical  bureau  on  the  Prussian  model. 

A  statistical-topographical  bureau  was  established  in 
Wurtemberg,  in  1820,  under  Memminger,  but  it  was  de- 
voted almost  exclusively  to  topographical  labors.  Statis- 
tics were  furthered  by  the  Verein  fur  Vaterlandskunde, 
founded  in  1822.  It  had  almost  an  official  character,  and 
published  its  transactions  in  Memminger's  Jahrbiicher, 
founded  in  1818.  In  1856  the  society  was  united  with  the 
bureau  into  a  real  statistical  organ. 

Baden  endeavored,  in  1836,  to  secure,  by  a  commission 
of  higher  officials  of  the  various  departments,  a  preparation 
of  its  administrative  statistical  material.  In  1852  a  statis- 
tical bureau  was  founded. 

The  Electorate  of  Hesse  collected  in  1842  and  1850  the 
materials  for  a  comprehensive  statistical  description  of  the 
country.     But  they  were  never  published  officially,  though 


History  of  Statistics.  59 

used  in  the  private  works  of  Pfister,  Landau,  and  Hilde- 
brand. 

Comprehensive  materials  were  collected  also  in  Hesse- 
Darmstadt,  but  they  were  not  prepared  till  after  the  estab- 
lishment, in  1861,  of  a  central  bureau  for  statistics. 

Similarly  the  older  returns  in  Oldenburg  were  prepared 
by  the  "  Statistische  Nachrichten,"  appearing  after  1855. 

Nassau  published  in  its  State  almanacs,  beginning  in 
18 19,  the  results  of  its  official  statistics. 

Hamburg  created  in  1844  a  Bureau  for  Indirect  Taxes 
ancf  Shipping,  which  published  from  1849  "  Hamburgs 
Handel  und  SchirTfahrt."  In  1866  another  bureau  for 
population  and  tax  statistics  was  established. 

In  1846  Bremen  organized  a  bureau  for  the  returns  of 
•  the  movement  of  trade,  which  gradually  enlarged  its  func- 
tions into  a  general  statistical  office. 

§  35.    THE   GERMAN   CUSTOMS   UNION   (ZOLLVEREIN). 

The  German  Customs  Union  was  of  the  greatest  impor- 
tance in  the  growth  of  German  statistics. 

The  customs  treaty,  of  October  25,  18 19,  between  Prussia 

and   Schwarzburg-Sondershausen   contains   all    essential 

I  ideas  of  this  preliminary  step  in  the  political  regeneration 

of  Germany,  and  among  them  certain  important  statistical 

requirements. 

The  uniform  custom  duties  collected  at  the  boundary  of 
the  State  which,  by  law  of  May  28,  18 18,  superseded  the 
former  provincial  customs  system  in  Prussia,  included  in 
the  customs  limits  parts  of  other  German  states.  Prussia, 
therefore,  proposed  to  divide  the  net  income  of  customs 
with  them  upon  the  basis  of  population.  The  fulfilment 
of  the  plan  required  a  triennial  census  of  population,  and 
a  uniform  system  of  internal  taxes  on  production  and  con- 
sumption. Sondershausen  accepted,  and  between  1823 
and  1826  most  of  the  Thuringian  and  Saxon  states  fol- 
lowed.    In  1828  the  Customs  Union  treaty  with  Hesse- 


60  Annals  of  the  American  Academy. 

Darmstadt  gave  rise  to  the  idea  of  a  common  administra- 
tion by  the  states  of  the  Union,  to  which  were  added  in 
1832  the  Electorate  of  Hesse  and  Homburg,  in  1833 
Bavaria  and  Wurtemberg,  and  in  1836  Nassau  and 
Frankfort-on-the-Main. 

The  foundation  of  a  uniform  census  of  population,  of 
exact  returns  concerning  revenue  and  expenditures,  and 
the  movement  of  merchandise  and  the  uniformity  in  various 
matters  relating  to  customs  and  taxes  constituted  the  sub- 
jects for  settlement  by  the  General  Conferences  in  affairs 
of  Customs  and  the  Union,  of  which  fifteen  took  place 
between  1836  and  1863,  and  of  which  the  discussions 
were  published.  The  statistical  returns  appeared  from 
1 84 1  in  20-30  pamphlets  yearly,  the  so-called  "  Commer- 
zialnachweisungen,"  which  were  carried  back  to  1834. 

As  far  as  possible,  it  was  sought  to  ascertain  for  each 
state  the  actual  consuming  population  in  each  year.  The 
resolutions  of  the  general  conferences  of  1834,  1843,  anc* 
1845,  which  abandoned  the  simple  distinctions  of  actual 
population  and  legal  population,  and  required  the  return 
of  the  resident  population,  led  to  great  difficulties  and  to 
the  utmost  complication  in  the  form  of  the  questions  to  be 
answered.  In  1845  tne  ordinance  required  that  the  enu- 
meration be  made  on  a  single  day,  the  3d  of  December, 
by  house  to  house  visitation,  and  with  the  return  of  each 
person  by  name. 

Tariff  politics  came  more  and  more  to  the  front,  particu- 
larly when  the  union  with  the  Tax  Union  of  Hannover, 
Brunswick,  and  Oldenburg  was  consummated  in  1852,  and 
during  its  discussion.  The  returns  concerning  trade  were 
therefore  extended,  and  industrial  statistics  resolved  upon. 
They  were  collected  in  1846,  and  on  a  larger  scale  in  186 1. 
From  i860  yearly  statistics  of  mines  were  published. 

After  the  treaty  of  July  8,  1867,  the  Customs  Parliament 
replaced  the  Customs  Union.  The  defects  and  faults  of  the 
existing  statistics  were  so  strongly  felt  that  the  Bundesrath 
agreed  to  the  appointment  of  a  commission  for  the  further 


History  of  Statistics.  6i 

development  of  the  statistics  of  the  Union.  Before  they 
could  complete  their  labors  the  constitution  of  the  German 
Empire,  of  April  16,  1 871,  united  all  the  German  states. 
But  from  their  investigations  were  determined  the  founda- 
tion and  sphere  of  action  of  the  Statistical  Office  of  the 
German  Empire,  established  July  21,  1872.  (Statistik  des 
deutschen  Reiches,  Bd.  I.,  1873,  Einleitung.— Meitzen  in 
(Holtzendorff)  Schmoller,  Jahrbuch  fur  Gesetzgebung  und 
Verwaltung,  I.,  1872  II.,  III.) 

§  36.    HOLLAND,    LUXEMBOURG,    AND   BELGIUM. 

In  Holland  the  published  reports  of  the  administrations 
of  finances  and  colonies  reach  back  to  an  early  date.  In 
1 80 1,  1806,  1829,  and  every  ten  years  since  a  census  of  pop- 
ulation has  taken  place,  and  in  18 16  and  1825  enumerations 
of  cattle.  A  statistical  bureau  under  Smits  and  a  statistical 
commission  were  established  in  1826;  but  both  of  these 
institutions  fell  to  pieces  when  Smits,  in  1830,  joined  the 
Belgian  uprising. 

By  the  treaty  of  February  8,  1842,  with  Prussia  (Preus- 
sische  Gesetzsammlung,  p.  92),  which  has  been  continued 
to  the  present  day,  the  Grand  Duchy  of  Luxembourg  was 
included  in  the  German  Customs  Union.  All  custom  laws 
and  ordinances  had  the  same  force  there  as  in  the  Rhine 
province.  Luxembourg  took  part,  therefore,  in  the  statis- 
tics of  the  Customs  Union. 

Holland  established  in  1848  a  statistical  bureau  in  the 
Ministry  of  the  Interior,  which  flourished  under  Baum- 
hauer  (died  1876),  but  was  replaced  in  1878  by  a  statistical 
commission,  as  the  greater  part  of  the  statistics  had  re- 
mained the  concern  of  the  various  departments. 

Belgium  in  1830  established,  under  Smits,  the  Direction 
de  la  statistique  generate  au  ministere  de  l'lnterieur.  The 
entirely  new  organization  of  the  state,  the  census  and  elec- 
tions of  1832,  and,  above  all,  the  law  of  May  1,  1843, 
whereby  the  state  undertook  the  construction  of  the  rail- 


62  Annals  of  the  American  Academy. 

roads,  with  the  consequent  struggles  and  decisions  on  the 
plan  to  be  pursued,  made  great  demands  on  the  official 
statistics.  This  led  to  the  development  of  an  intense 
activity  in  various  fields. 

In  1 84 1  Quetelet,  who  had  the  supervision  of  statistics 
in  the  ministry,  created  the  Central  Commission  for  Statis- 
tics. It  was  composed  of  officials  and  scholars,  and  its 
valuable  deliberations  were  published,  after  1843,  in  the 
Bulletin  de  la  commission  de  la  statistique  beige.  Pro- 
vincial commissions  supervised  the  collection  of  the  data. 
The  preparation  for  the  general  census  of  October  15, 
1846,  is  to  be  noted  as  the  turning-point  in  the  ideas  as  to 
stricter  methods  for  all  kinds  of  statistical  returns.  This 
census  of  1846  (population,  agriculture,  industry)  was  the 
first  of  the  series  of  enquetes  of  1856,  1866,  1876,  and  1880. 
Besides  this,  the  work  "  Statistique  generate  de  la  Belgique, 
expose  de  la  situation  du  royaume,"  in  1852,  gave  a  de- 
scription of  the  development  of  the  country  in  the  ten 
years  from  1840  to  1850.  Since  then  it  has  been  con- 
tinued in  decennial  periods. 


§  37.   AUSTRIA-HUNGARY. 

The  establishment  of  a  topographical-statistical-  bureau 
for  the  Empire  was  proposed  in  18 10  and  18 19,  but  not 
carried  out  until  1829,  by  the  General  Auditing  Depart- 
ment, under  v.  Metzburg  (died  1839).  At  that  time  104 
tables  and  charts  were  prepared  from  the  material  of  the 
previous  year,  and  100  copies  of  them  in  writing  were 
distributed  among  the  various  governmental  offices.  The 
repetition  ordered  in  1830  covered  the  period  subsequent 
to  1 8 19.  A  hand-book  on  the  state  of  the  realm  was  pre- 
pared in  1830. 

Freiherr  v.  Kubeck  secured  an  imperial  order  of  March 
31, 1840,  creating  the  Direction  of  Administrative  Statistics 
as  an  independent  body.    Lucam  was  the  first  director,  his 


History  of  Statistics.  63 

successors  1841-66,  v.  Czornig  (born  1804),  Fricker,  and 
v.  Inama-Sternegg. 

It  was  not  until  1845  that  publication  of  the  returns  was 
permitted,  and  then  only  for  selected  portions.  In  1846 
the  "Tafeln  zur  Statistik  der  oesterreichischen  Monarchie 
fur  1842  "  appeared.  Up  to  1853  four  other  works,  contain- 
ing the  data  for  the  years  1843-48,  followed.  After  the  trans- 
fer in  1848  of  the  statistical  work  to  the  Ministry  of  Trade, 
a  new  series  of  tables  on  Territory,  Population,  Adminis- 
tration of  the  state,  and  civilization,  began  with  1849.  The 
customs  administration  published  from  1840,  reports  of  the 
movement  of  trade.  After  1859  there  appeared  from  the 
Ministry  of  Finance  reports  on  the  finances.  Nevertheless 
centralization  of  the  official  statistics  remained  the  rule, 
and  this  was  continued  under  the  Statistical  Central  Com- 
mission, created  in  1863,  except  in  so  far  as  after  1867  it 
was  limited  to  the  kingdoms  and  countries  represented  in 
the  Reichsrath.  In  1872,  however,  a  statistical  department 
was  formed  in  the  Ministry  of  Trade,  and  in  1873  in  the 
Ministry  of  Agriculture. 

The  Hungarian  statistics  have  been  prepared  since  1867 
by  a  statistical  bureau  in  Buda-Pesth.  Centralization  is  here 
the  rule,  according  to  a  law  of  1874.  In  1868  a  statistical 
central  commission  was  formed  here  also. 

§  38.    GREAT    BRITAIN. 

No  other  country  gave  such  early  and  extensive  pub- 
licity to  its  statistics  as  Great  Britain.  The  Parliamentary 
papers  mentioned  in  §  10  are  in  addition  to  the  reports  of 
revenue  and  expenditures,  very  rich  in  reports  from  offi- 
cials, and  Parliamentary  Commissions,  on  the  various 
questions  which  engage  the  attention  of  Parliament. 
These  often  led  to  annual  repetitions,  and  had  as  a  con- 
sequence the  establishment  of  statistical  departments,  such 
as  that  in  the  Board  of  Trade  1832,  and  in  the  Home  Office 
1834. 


s/ 


64  Annals  of  the  American  Academy. 

The  proposal  of  a  general  census  of  population  was  first 
made  in  1753,  but  was  not  acted  upon.  When  renewed  in 
1800,  it  was  agreed  to.  It  was  decided  that  the  census 
should  take  place  every  ten  years.  The  first,  under  the 
charge  of  Rickmann,  took  place  in  1 80 1.  With  it  was 
required  an  abstract  from  the  parish  registers,  giving  the 
number  of  baptisms  and  funerals  for  every  decade  from 
1700  to  1750,  and  for  every  year  after  the  last  named. 
From  them  Finlaison  calculated  backward  the  population 
of  England  in  1700  at  5,131,516  souls. 

The  returns  of  1801  distinguished  simply  sex,  pos- 
session of  a  house,  and  chief  occupation  in  agriculture, 
commerce,  manufacture,  or  as  an  artisan.  Gradually  the 
questions  were  increased.  The  return  of  age  was  in  182 1 
voluntary,  and  in  1841  the  attempt  was  made  to  obtain  the 
ages  in  certain  classes — twenty-year  periods  for  the  rural 
and  five-year  periods  for  the  urban  population.  The  census 
of  185 1,  however,  attained  a  high  degree  of  completeness. 

Returns  of  the  movement  of  population  were  first  re- 
|  quired  from  the  parishes  in  England  in  1800,  in  Scotland 
1807,  and  in  Ireland  18 10.  The  numerous  sects  necessitated 
the  registration  by  the  state.  The  law  of  August  17,  1836 
(6  &  7  Will.  IV.  Ch.  36),  for  England  and  Wales  required 
the  commissioners  of  the  poor  to  establish  registration 
districts,  with  registrars  responsible  to  a  superintendent. 
From  every  registry  a  copy  is  sent  to  the  Registrar-General 
in  London,  in  whose  office  they  are  carried  into  the  Gen- 
eral book  accessible  to  the  public.  Similar  institutions 
were  created  in  Scotland  1854  (17  &  18  Vict.  Ch.  80),  and 
in  Ireland  1863  (26  Vict.  Ch.  11). 

The  Registrar-General's  office  has  since  received  charge 
of  the  census,  formerly  the  work  of  special  commissions, 
and  in  Ireland  also  of  the  statistics  of  agriculture. 

In  England  and  Scotland  statistical  societies  undertake 

I  the  collection  and  preparation  of  agricultural  and  other 

\  statistics.     The  Manchester  Soceity  was  founded  in  1833. 

The  London  Society,  which  includes  almost  all  statistical 


History  of  Statistics.  6$ 

Aj  authorities  of  the  country,  and  has  published  since  1838  a 
J  valuable  journal,  was  founded  in  1834.     The  great  agricul- 
*  tural  Enquete  for  the  United  Kingdom,  in  1879-82,  was  the 
work  of  a  Parliamentary  Commission  on  Agricultural  In- 
terests. 

§  39.    UNITED    STATES   OF   AMERICA. 

The  English  colonies  in  North  America  had  an  obvious  x 
interest  in  ascertaining,  even  earlier  than  the  mother  coun- 
try, the  number  of  their  population.  Data  on  the  subject 
reach  as  far  back  as  1607  for  Virginia,  1700  for  South  Car- 
olina, and  1 7 10  for  North  Carolina.  In  all  the  British  pos- 
sessions in  North  America  1,083,000  souls  were  enumer- 
ated in  1753, 

The  Constitution  of  September  17,  1787,  prescribed  as 
a  legal  basis  of  the  elections  an  actual  enumeration  of  the 
population  within  three  years,  and  a  repetition  every'"" 
successive  decade.  Poll  taxes  and  other  direct  taxes  cart 
be  laid  only  in  accordance  with  the  population  thus  ascer- 
tained. The  first  census  took  place  in  1790,  and  has  since 
been  continued  regularly.  It  is  the  concern  of  the  National 
Government,  and  was  carried  out  before  1880  by  the  United 
States  Marshals.  Besides  the  enumeration  of  the  popula-v 
tion,  the  census  contains  statistics  on  the  movement  of 
population,  on  agricultural,  industrial,  commercial,  and 
other  economic  relations. 

The  Constitution  further  provides  that  Congress  shall 
legislate  on  finance,  currency,  national  defence,  and  gene- 
ral welfare,  and  that  all  duties  and  taxes  shall  be  uniform.. 
The  care  of  the  postal  service  and  the  regulation  of  patents, 
are  in  the  hands  of  the  Union.  From  these  functions,  and 
from  the  right  of  supervision  vested  in  Congress,  there  has 
arisen  a  mass  of  public  documents,  as  in  England,  full  of 
reports  and  statements.  The  necessity  of  a  permanent 
statistical  office  has  not  been  felt  until  recently.  The  work 
of  the  census  is  carried  on  in  bureaus  organized  for  the 
purpose.  A  law  of  1866  created  a  statistical  bureau  for 
5 


66  Annals  of  the  American  Academy. 

(  commerce  and  shipping  in  the  Department  of  the  Treasury. 

The  United  States  Bureau  of  Labor  has  issued  valuable 

statistical  reports  since   1886,  and  in  the  publications  of 

other   government   offices,  to  which  reference  has  been 

made,  much  material  is  to  be  found. 

Many  of  the  states  have  established  bureaus  for  labor 

statistics,  which  have  furnished  some  excellent  studies. 
j  A  prosperous  statistical  society,  the  American  Statistical 

Association,  founded  in  1839  in  Boston,  is  doing  good 

work  for  statistics. 

§  40.  DENMARK,  NORWAY,  AND  SWEDEN. 

Before  1833  all  statistical  data  in  Denmark  were  govern- 
ment secrets.  Among  the  general  public,  neither  the 
value  of  imports  and  exports,  nor  the  results  of  the 
financial  administration  were  known.  Nevertheless,  a 
census  of  population  occurred  in  1769,  and  in  1801  for  the 
kingdom  and  the  Faroe  Islands,  and  in  1803  and  18 10  for 
Schleswig  and  Holstein. 

In  1 83 1  representation  of  the  estates  had  been  intro- 
duced, and  in  1833  tne  king  appointed  a  commission  of 
higher  officials,  who,  without  a  special  bureau,  published 
18  volumes  of  tables  on  all  branches  of  statistics  between 
1833  and  1849.  In  x^49  with  the  constitution  a  statis- 
tical central  office  was  established,  whose  chief  was  to 
have  a  voice  in  all  statistical  questions  which  might  arise 
in  the  various  departments.  The  bureau  continued,  aside 
from  the  separation  of  Schleswig-Holstein,  the  former 
tables,  and  united  the  statistics  of  the  country,  so  that 
now  only  medical  statistics  are  in  other  hands,  a  com- 
mittee of  the  Royal  Medical  Society. 

Sweden  and  Norway  built  up  their  official  statistics  of 
population  chiefly  on  a  thorough  and  exact  preparation  of 
the  parish  registers,  which  had  existed  (§  19)  in  Sweden 
since  1749.  In  Norway  a  general  census  of  the  population 
occurred  in  1801  and  in  1845.     F°r  tne  greater  part  of  the 


v 


History  of  Statistics.  67 

administrative  statistics,  and  particularly  for  the  agricul- 
tural returns,  reports  of  the  chief  branches  were  published 
every  five  years  after  1830  in  both  kingdoms.  A  suitable 
preparation  of  these  reports  in  connected  form  was  pro- 
posed as  early  as  1839. 

For  this  purpose,  in  1846,  a  statistical  bureau  was  at- 
tached to  the  Ministry  of  the  Interior  in  Norway.  It 
publishes  statistical  tables  of  the  kingdom.  In  addition, 
medical  statistics  have  been  published  since  1827,  and 
finance  reports  since  1838. 

In  Sweden  statistical  bureaus  were  established  in  1830 
in  the  Ministries  of  Trade  and  Justice.  Since  185 1  have 
appeared  the  "  Contributions  to  the  Official  Statistics  of 
Sweden,"  which  contain  the  publications  of  the  various 
departments.  A  statistical  central  office  was  established 
in  1857  and  united  with  the  Tables  Commission. 


§41.    RUSSIA. 

An  ordinance  of  1802  prescribed  in  Russia  for  the  eight 
newly  established  ministries  the  collection  and  publication 
of  statistical  data  and  periodical  reports.  At  that  time 
were  begun  the  publications  of  certain  departments,  par- 
ticularly the  tables  of  foreign  trade  and  shipping,  which 
have  not  been  interrupted.  Further  facts  may  be  found  in 
the  annual  report  of  Minister  Kotschubey  in  1804,  pub- 
lished in  Storch's  journal. 

In  1 83 1  Pogodin  investigated  historically  the  reports 
which  had  been  required  as  early  as  the  time  of  Peter  the 
Great.  In  1833  it  was  ordered  that  proper  subjects  from 
his  work,  at  least  in  outline,  should  be  published. 

In  1834  statistical  committees  were  formed  in  the  gouv- 
ernements,  consisting  of  the  chiefs  of  departments  and 
members  chosen  by  the  committee,  with  the  Civil  Gov- 
ernor as  president.  The  results  were  sent  for  further 
preparation  to  the  statistical  department  of  the  Ministry 


V' 


68  Annals  of  the  American  Academy. 

of  the  Interior,  which  beginning  in  1843  published*"  Ma- 
terials for  the  Statistics  of  the  Russian  Empire." 

In  1852  a  central  statistical  commission  was  created  in 
the  same  Ministry.  At  the  same  time  there  existed  sta- 
tistical sections  in  the  Ministries  of  Finance  and  Agricul- 
ture, and  since  1853  a  statistical  committee  in  the  admin- 
istration of  roads,  transportation,  and  public  buildings. 
The  central  commission  published,  in  i860,  "Tables  of  the 
Russian  Empire,"  and  since  1866  regularly  the  statistics 
of  the  empire.  Besides  these  there  are  the  publications  of 
the  various  departments.  However,  actual  returns  even  of 
population  are  so  difficult  to  obtain  that  the  data  for  the 
greater  number  of  the  gouvernements  rest  not  upon  actual 
enumeration,  but  merely  on  the  reports  of  officials  and 
committees. 

§42.   SWITZERLAND,    ITALY,   SPAIN,    PORTUGAL,   AND    GREECE. 

In  Switzerland  some  of  the  cantons  had  enumerations 
of  population  very  early,  at  least  at  the  beginning  of  the 
present  century.  In  1836  a  table  of  the  results  for  all 
cantons  was  published.  Before  1848  common  statistics  for 
all  Switzerland  could  only  be  obtained  on  trade  and  cus- 
toms. The  Federal  law  concerning  the  organization  of 
the  Federal  Council  of  May  16,  1849,  designates  the  col- 
lection of  statistics  as  one  of  the  functions  of  the  latter. 
In  1850  a  general  census  of  population  took  place,  and 
was  prepared  by  Franscini  for  publication  in  Vol.  I.  of  the 
"  Beitrage  zur  Statistik  der  schweizerischen  Eidgenossen- 
schaft."  But  without  money  and  executive  power  over 
the  cantons  the  federal  statistics  of  the  movement  of  the 
population  proved,  in  1852,  to  be  impracticable.  The 
Federal  law  of  January  21,  i860,  improved  this  state  of 
affairs,  though  it  limited  the  obligation  of  the  cantons  to 
enumerations  of  population  and  cattle.  Since  then  a  Fed- 
eral Statistical  Bureau  is  in  operation. 

In  Italy  (§  24)  there  was  always  the  greatest  interest  for 


History  of  Statistics.  69 

statistics,  but  Zuccagni-Orlandini  shows  in  his  "  Corografica 
Italica"  (1835-1845)  how  nearly  impossible  it  was  to  com- 
bine the  data  of  the  numerous  states.  (Caesare  Correnti 
in  Annuario  Statistico  Italiano  for  1857-58.)  Sardinia  had 
a  Commissione  superiore  di  statistica  which  published  the 
census  in  18 19  and  1838  with  comparisons.  In  1842  ap- 
peared Avet's  "  Statistica  giudiciaria,"  which  was  continued 
in  1852  and  1857  by  a  special  commission  for  civil  and 
criminal  justice.  Tuscany  collected  annually  by  means  of 
a  central  bureau  the  movement  of  the  population,  and 
founded  under  Zuccagni,  1849,  a  Direzione  di  statistica 
generale.  Sicily  received  as  early  as  1832  a  statistical 
bureau,  the  continental  part  of  the  kingdom  in  185 1. 
Parma  was  described  from  official  sources  by  Molossi, 
and  Modena  by  Roncaglia,  in  1829.  For  Rome  the  census 
of  the  population  of  1853  was  prepared  by  Grisi.  The 
data  then  extant  were  collected  in  1862  in  the  official 
work,  Censimento  degli  antichi  stati  Sardi  e  censimenti 
di  Lombardia,  di  Parma,  et  di  Modena. 

Since  the  foundation  of  the  kingdom  of  Italy  statistics 
have  gained  in  uniformity  and  in  extent  and  importance. 
In  1 86 1  a  statistical  bureau,  and  in  1868  a  statistical  cen- 
tral commission  were  established.  The  Statistica  del 
Regno  d'ltalia  appears  since  1864  in  numerous  volumes, 
and  besides  these  there  are  the  extensive  publications  of 
the  various  departments.  The  Direzione  della  Statistica 
had  been  attached  to  various  Ministries,  but  as  a  rule,  and 
permanently  since  1878,  to  the  Ministero  di  agricultura 
industria  et  commercio.  The  director  was  until  1872 
Maestro,  since  then  Bodio  (born  1840). 

In  Spain  (§  24)  periodical  statements  of  trade  with  for-^ 
eign  countries  and  with  the  colonies  exist  since  1849.  In 
1856  a  Direcion  general  de  estadistica  was  established,  and 
reorganized  by  law  of  June  5,  1859.  I*  began  in  1859  the 
publication  of  an  Annuario  estadistico.  Before  this  we 
have   only  a  few  private  works,  such  as  the  Diccionarii 


yo  Annals  of  the  American  Academy. 

estadistici  of  Minano,  1826,  Madoz,  1846,  and  de  Plaza, 
1852,  which  were  based  on  official  sources. 

For  Portugal  there  appeared  in  18 17  a  Diccionario,  and 
in  1822  a  statistical  description  by  Balbi.  The  different 
Ministries  among  which  the  statistics  are  divided,  published 
only  a  few  details.  The  Ministry  of  the  Interior  under- 
took a  census  of  population  in  the  years  1838,  1843,  1849, 
and  1850.  In  1857  a  statistical  central  commission  was 
established,  and  in  the  year  1859  a  statistical  bureau  in  the 
Ministry  of  Trade  and  in  i860  in  the  Ministry  of  War. 

In  Brazil  a  census  of  population  was  attempted  in  18 17, 
and  repeated  in  1872. 

Greece  incorporated,  at  the  organization  of  the  state  in 
1834,  a  statistical  bureau  in  the  economic  section  of  the 
Ministry  of  the  Interior.  It  has  published  since  1861  the 
ics  of  Greece. 

onceptions  of  the  Method  and  Purpose  of 
Statistics. 

§43.  influence  of  official  statistics. 

The  development  of  official  statistics  in  the  most  impor- 
tant countries,  the  participation  of  numerous  statistical  and 
other  offices,  the  occupation  of  trained  statisticians  in  the 
service  of  the  state,  have  all  combined  to  make  this  par- 
ticular branch  of  statistical  activity  the  predominant  one. 

In  the  nature  of  things  there  was  a  certain  limitation,  a 
one-sided  specialization  in  these  labors  of  the  official  insti- 
tutions. Their  functions  must  be  exercised  rather  as  an  art 
than  as  a  science.  Their  work  is  divided  up  for  immediate 
practical  purposes  into  a  host  of  changing  single  problems, 
and  the  more  successfully  the  special  effort  attains  its  goal 
the  weaker  becomes  the  incentive  to  seek  for  underlying 
reasons  and  general  interdependence.  Special  branches 
of-St»tistical  practice  csu!d  therefore  undergo  quite   an 


History  of  Statistics.  71 

independent  and  individual  development.  They  could 
indeed  receive  a  more  or  less  complete  theoretical  foun- 
dation, and  yet  the  science  as  a  whole  lack  entirely  the 
necessary  uniformity  and  simplicity  of  a  theoretical  basis 
and  the  needed  rounding  off  of  its  sphere  of  ideas.  \\  The 
development  of  the  technique,  its  adaption  to  the  end  in 
/  view,  and  its  application  under  given  circumstances  were 
the  results  of  the  work  of  the  official  institutions  in  this 
periods  The  acute  criticism  of  a  man  like  Hoffmann  had, 
therefore,  no  pronounced  tendencies  for  any  line  of  theory. 
Almost  averse  to  all  theoretical  exposition,  he  drew  his 
conclusions  with  remarkable  simplicity  and  directness. 
His  critical  demands  scarcely  appear  to  us  to-day  as 
particularly  remarkable,  but  at  the  time  they  were  new 
and  led  to  great  innovations.  Their  tone  seems  to  us 
modest  and  reserved,  but  the  reason  is  to  be  found  in 
the  limited  means  and  the  undeveloped  processes  of  secur- 
ing returns  of  that  day. 

Every  conclusion  of  empirical  science  is  based  on 
I  something  which  must  be  assumed  as  fixed  and  known. 
■  This,  however,  may  be  open  to  question,  and  we  may,  of 
course,  go  on  indefinitely  calling  into  question  the  basis 
of  the  reasoning.  Nevertheless  somewhere  in  this  course 
these  critical  doubts  must  be  considered  as  removed ;  but 
this  point  is  determined  only  gradually,  but  as  time  goes 
on  more  and  more  thoroughly  by  theory  and  practice. 
The  progress  of  criticism  is  hesitating  because  more  exact 
demands  are  conditioned  upon  more  exact  means  for  their 
realization. 

Preoccupation  with  the  specific  problem  to  be  solved, 
criticism  of  the  results  rather  than  the  origin  of  the  data,  1 
and  a  certain  empiricism  in  the  conception  of  the  method 
are  the  predominating  characteristics  of  the  official  statis- 
ticians of  the  period.  The  same  is  also  true  of  the  private 
persons  who  devoted  themselves  to  the  statistical  descrip- 
tion of  countries  or  comparisons  of  them,  as  Padovani 


72  Annals  of  the  American  Academy. 

(1817),  Balbi  (1822),  v.  Malchus  (1826),  Schubert  (1835-48), 
Frhr.  v.  Reden  (1846),  and  others. 

1 44.  perfecting  of  sussmilch's  statistics. 

Sussmilch's  statistics,  by  their  special  field  of  investiga-  . 
tion,  were  obviously  limited  to  the  numerical  conception/ 
and  treatment  of  their  data,  and  were  theoretically,  there- 
fore, the  most  developed.  This  was  not  because  they  had 
successfully  surmounted  greater  difficulties,  but  rather 
because  the  limited  field  permitted  more  facile  demon- 
strations, and  therefore  a  certain  completeness  in  their 
conclusions.  The  details  of  the  investigations  concerned 
only  a  small  sphere  of  phenomena.  It  naturally  suggested 
itself  therefore  to  note  the  coincidences  or  divergences  of 
the  results,  to  observe  their  continuity,  and  to  draw  con- 
clusions as  to  the  causes  and  effects  of  these  facts.  !  It 
followed  as  a  matter  of  course  that  the  clear  numerical 
relations  should  become  the  subject  of  consideration  and 
lead  to  the  attempt  to  ascertain  further  regularities. 

Among  the  works  may  be  mentioned : 

18 14.  Laplace  (born  1749,  died  1827),  Essai  philoso- 
phique  sur  les  probabilites,  quite  in  the  line  of  the  views 
expressed  by  Condorcet  (§  19). 

1821-29.  Fourier  (born  1768,  died  1829,  physicist),  No- 
tions generates  sur  la  population,  and  two  Memoires  sur 
les  resultats  moyens,  etc.,  appendices  to  Recherches  sta- 
tistiques  sur  la  ville  de  Paris  and  to  the  census  of  Paris  of 
18 17  (§  23).  In  these  he  states  the  first  algebraic  formula 
for  calculating  mortality  tables  in  a  stationary  population, 
and  calls  attention  to  the  differences  in  the  calculation  re- 
sulting from  taking  whole  years  or  dividing  the  years  into 
sections.     (Knapp,  p.  78;  see  §  11.) 

1825-37.  J.  C.  Casper  (born  1796,  died  1864,  Medizinal- 
rath  in  Berlin),  Beitrage  zur  medizinischen  Statistik. 

1826.  L.  R.  Villerme  published  an  investigation  of  the 
monthly  distribution  of  conceptions  and  births  in  their 
relations  to  climate,  labor,  nutriment,  customs,  etc. 


History  of  Statistics.  73 

1839.  Ludw.  Moser  (professor  in  Konigsberg),  Gesetze 
der  Lebensdauer.  This  criticises  keenly  the  results  of 
preceding  work,  and  establishes  precise  propositions  as 
to  various  methods  of  calculation  and  interpolation,  mor- 
tality in  various  classes  and  positions  in  life  in  a  non- 
sfationary  population,  and  in  the  relations  of  marriages, 
conceptions,  births,  stillbirths,  widowhood,  as  well  as  life 
and  annuity  insurance,  tontines,  etc. 

In  1842  Hermann  (§  34)  began  in  Bavaria  his  attempt  to 
ascertain  the  mortality  by  direct  observation  of  the  deaths 
of  persons  born  in  a  given  calendar  year. 


§45.    PAUPERISM   AND   QUETELET'S   WORK    ON    MAN. 

The  study  of  population  was  broadened  by  certain  con- 
temporaneous conditions  and  circumstances  into  a  philo- 
sophical and  sociological  treatment  of  moral  statistics. 

About  the  end  of  the  third  decade  of  the  present  century 
the  fear  of  over-population,  which,  based  on  the  ideas  of 
Malthus,  had  its  origin  in  England,  became  general.  In 
1828  de  Gerando  wrote  "  La  visitateur  des  pauvres."  The 
preparatory  labors  for  the  English  poor  law  of  1834  be- 
came well  known.  Between  1834-36  numerous  works  on  • 
pauperism  appeared  by  Jiirgen-Hanssen,  v.  Liittwitz,  Gode- 
froy,  Villeneuve-Bargemont,  Heiberg,  Senior,  Schmidt, 
Duchatel-Neuville.  In  1832  Fourier  published  the  peri- 
odical "  Phalangstere."  The  general  tendency  of  thought 
is  reflected  in  the  successes  of  the  novels  of  Alexander 
Dumas  and  Eugene  Sue.  In  1839  "  Les  crimes  celebres  " 
appeared,  and  in  1842  "  Les  mysteres  de  Paris." 

With  the  increasing  consciousness  of  human  community 
awoke  also  the  feeling  of  the  contrasts  of  society,  which, 
however,  degenerated  into  a  specious  apologetic  of  moral 
offences.  Crime  was  treated  as  an  unavoidable  conse- 
quence of  untenable  social  conditions,  and  in  this  way  an 
approach  was  made  to  those  conceptions  of  population 


V. 


74  Annals  of  the  American  Academy. 

statistics  which  regard  the  numbers  as  evidence  of  natural 
laws. 

The*  first  representatives  of  moral  statistics,  Francis 
d'lvernois,  in  his  investigations  of  the  comparative  mo- 
rality of  nations,  1833,  and  Guerry,  in  his  essay  on  the 
moral  statistics  of  France,  1834,  perceive  in  the  constancy 
of  the  numbers  nothing  more  than  the  influence  of  con- 
stant factors  and  conditions. 

A  confirmation  of  these  views,  and  at  the  same  time  a 
more  profound,  more  humane,  and  more  interesting  expo- 
sition of  them  was  given  in  Quetelet's  work,  "Sur  l'homme 
et  le  developpement  de  ses  facultes  ou  essai  de  physique 
social,"  which  appeared  in  this  agitated  period,  in  1835. 

Lambert  Adolphe  Jacques  Quetelet  (born  1796  at  Ghent, 
died  1874,  1 8 14  professor  of  mathematics,  1828  director  of 
the  observatory  at  Brussels)  published  in  1829  Recherches 
statistiques  sur  le  Royaume  de  Pays  Bas,  and  was  appointed 
chief  of  the  Belgian  statistics  (§  36). 

His  work,  Sur  l'homme,  declares  expressly  the  constant 
averages  in  moral  statistics  to  be  a  proof  that  the  actions 
of  mankind  are  regulated  by  laws.  Among  individuals  the 
natural  forces  which  tend  toward  the  preservation  of  these 
laws  are  indeed  influenced  by  disturbing  forces  resulting  in 
accidental  and  individual  phenomena.  In  the  totality  of 
mankind,  however,  the  laws  clearly  appear.  They  are  not 
however  inalterable,  but  dependent  on  existing  societary 
conditions.  Natural  influences  are  more  or  less  counter- 
acted by  others,  the  products  of  civilization.  The  general 
and  periodic  influences  are  more  effective  than  the  indi- 
vidual ones.  In  all  cases  an  average  standard  is  the  best,^, 
and  is  obtainable  statistically.  The  average  man  would, 
it  is  true,  be  different  at  every  period,  but  would  neverthe- 
less represent  a  state  of  equilibrium,  the  true  type  of  the 
totality  of  operating  influences.  Man  advances,  however, 
by  his  intelligence  to  a  condition  no  longer  that  of  nature. 
Virtue,  like  nature,  is  unchangeable,  but  the  intelligence 
of  mankind  develops  just  as  does  that  of  individuals.     All 


History  of  Statistics.  75 

individual  development  is  determined  by  the  conditions  of 
society,  by  the  course  of  great  events.  Society  is  respon- 
sible for  the  criminal  as  well  as  for  the  great  man.  The 
criminal  is  merely  the  instrument  of  society.  He  is  the 
propitiatory  sacrifice  of  society ;  his  crime  the  fruit  of  the  * 
conditions  under  which  he  lives. 

Quetelet  nevertheless  excludes  any  thought  of  fatalism 
(Letters  a  S.  A.  le  due  de  Saxe-Coburg,  1846).  He  sees 
the  workings  of  law  merely  in  the  phenomena  of  the  great  ' 
masses,  and  denies  expressly  any  constraining  force  on  the 
individual.  But  it  cannot  be  denied  that  he  does  not  solve 
the  contradiction,  and  that  he  does  not  speak  clearly  as  to 
the  responsibility  of  the  individual  for  his  actions. 

The  masterly  book  found  a  warm  reception,  more  among 
the  general  public,  it  is  true,  than  among  the  statisticians. 
The  latter  could  not  fail  to  perceive  the  weak  points  in  the 
deductions  and  in  the  idea  of  the  average  man.  But  the 
depth  and  moderation  of  his  views  and  the  noble  humanity 
of  his  spirit  won  for  the  author  great  personal  influence 
and  regard  among  them,  which  he  preserved  till  his  death. 

§46.    CONCEPTIONS    OF   STATISTICAL   THEORY. 

If  we  mean  by  theory  the  fundamental  idea  from  which 
the  varied  contents  of  a  sphere  of  knowledge  recognized 
as  homogeneous  can  be  uniformly  understood  and  sys- 
tematically grouped  in  the  circle  of  general  knowledge, 
then  we  may  see  already  the  beginnings  of  such  penetra- 
tion into  the  material  and  processes  of  statistical  investi- 
gation. 

The  train  of  thought  in  Achenwall's  school  was  directed 
merely  toward  the  description,  comparison,  and  examina- 
tion of  a  certain  mass  of  essential  conditions  in  various 
single  states.  The  contents  of  the  numerous  theories  of 
statistics  which  emanated  from  the  school,  and  which  ap- 
peared to  them  to  exhaust  the  subject,  consisted  simply  in 
the  systematic  arrangement  of  these  particular  data. 


j6  Annals  of  the  American  Academy. 

When,  however,  the  table  statisticians  brought  forward 
the  idea  that  the  examination  of  the  "Staatsmerkwurdig- 
keiten  "  cannot  be  fruitful  without  distinct  numerical  meas- 
urements, the  consequence  was  obvious  that  the  essence 
of  statistics  must  be  sought  in  this  measurement  of  phe- 
nomena. Thus  the  idea  of  a  distinct  methodical  procedure, 
,  which  had  thus  far  been  limited  to  the  calculation  of 
probabilities,  was  greatly  extended  in  its  scope.  F.  J. 
Mone  (Theorie  der  Statistik,  1824)  says  in  this  view  of 
things,  "  The  method  of  statistics  is  the  art  or  science  of 
uniting  as  a  whole  all  statistical  material.  For  this  pur- 
pose the  materials  must  be  sought,  collected,  classified, 
ordered,  arranged,  and  combined,  in  order  to  make  a  single 
or,  so  to  speak,  an  organized  entirety." 

Melchior  Gioja  (§  24)  presented  in  1826  in  his  Filosofia 

della  statistica,  a  well-developed  system  on  the  nature  and 

the  evidential  value  of  the  indications,  which  permit  con- 

,   elusions  as  to  certain  conditions  and  influences,  and  as  to 

the  causes  and  intensity  of  these  influences. 

His  friend  Romagnosi  demonstrated  in  1827  and  1828 
in  Questioni  sull'  Ordinamento  delle  statistiche  (Annali 
universali  di  statistica,  Vol.  XIV.),  that  every  statistical 
problem  requires  for  its  solution  a  well-considered  plan, 
"~  exact  execution  of  the  necessary  observations,  examination 
and  scrutiny  of  the  results  obtained,  and,  finally,  conclu- 
sions capable  of  demonstration. 

The  London  Statistical  Society  in  its  programme  of  1838 
(Journal,  Vol.  I.,  1838),  declares  that  the  discussion  of 
cause  and  effect  is  not  within  the  province  of  statistics. 
"  It  is  not,  however,  true  that  the  statist  rejects  all  deduc- 
tions, or  that  statistics  consist  merely  of  tables  of  figures ; 
it  is  simply  required  that  all  conclusions  should  be  drawn 
from  well-attested  data,  and  shall  admit  of  mathematical 
demonstration." 

•About  the  same  time  Potlock  (an  address  explanatory 
of  the  objects  and  advantages  of  statistical  inquiries,  1838) 


History  of  Statistics.  jy 

declared  that  all  actual  things,  or  facts,  qualities,  and  the 
like  which  could  be  collected  in  numbers  were  statistics. 

Cournot  (Exposition  de  la  theorie  des  chances  et  des 
probabilitees,  1843)  understands  as  statistics  the  science 
which  has  for  its  subject  the  collection  and  comparison  of 
numerous  facts  of  every  kind,  with  the  purpose  of  ascer- 
taining the  numerical  relations  which  appear  independent 
of  accidental  exceptions,  and  thus  denote  the  presence  of 
regular  causes  whose  effects  are  combined  with  those  of 
accidental  causes. 

Moreau  de  Jonnes  (§  33)  says  (1847)  briefly  statistics 
is  the  science  of  social  facts  expressed  in  numerical  terms. 

Yet  all  these  obvious  advances  in  the  conception  of  the 
theory  were  isolated.  In  addition  to  the  traditional  ideas 
of  the  State  statistics,  we  now  have  Quetelet's  almost 
mystical  hopes  of  finding  in  the  statistical  figures,  laws  of 
the  cosmological  order,  and  of  the  world's  history,  and  of 
making  this  aim  the  fundamental  principle  of  statistics. 

At  that  time  J.  Fallati  (born  1809,  died  1855)  attempted 
in  his  "  Einleitung  in  die  Wissenschaft  der  Statistik " 
(1843)  to  determine  the  real  conception  of  statistics.  It 
seems,  however,  that  although  he  makes  some  important 
distinctions,  and  shows  some  insight  into  important  prob- 
lems, his  explanation  of  the  essence  of  statistics  remains 
obscure. 

There  was  so  much  confusion  among  these  contradictory    * 
views  that  in  1847,  at  the  instance  of  Fallati,  Schubert  and 
v.  Reden,  a  special  commission  to  investigate  them  was 
appointed  by  the  Germanisten-Versammlung,  founded  in 
1846. 

This  state  of  affairs  led  A.  A.  Knies  (born  1 821)  to  write 
"  Die  Statistik  als  selbststandige  Wissenschaft,  zur  Losung 
des  Wirrsals  in  Theorie  und  Praxis  dieser  Wissenschaft.',   u 
He  proposes  to  exclude  from  statistics  proper  the  statistics  \ 
of  Achenwall  as  merely  historical,  and  to  hold  fast  to  the   \ 
political  arithmetic,  which  should  be  developed  by  exact 
mathematical  methods. 


7$  Annals  of  the  American  Academy. 


D.  THE   DEVELOPMENT  AND   PREDOMINANCE  OF  THE 
STATISTICAL  METHOD. 

I.  The  International  Statistical  Congress. 

§47.   OCCASION,   ORGANIZATION,    AND   DURATION    OF  THE 
CONGRESS. 

The  prevailing  confusion  in  regard  to  the  scientific  de- 
velopment of  statistics  was  removed  to  such  an  extent  by 
the  International  Congress,  that  this  forms  a  decisive 
turning-point  for  theory  and  practice. 

The  plan  of  the  Congress  was  formed  in  185 1,  at  the 
London  Industrial  Exposition,  by  Quetelet,  Vischer,  Dupin, 
Farr,  Porter,  Fletcher,  Kennedy,  and  others.  On  account 
of  the  interesting  features  in  the  Belgian  statistics  (§  36) 
Brussels  was  fixed  upon  as  the  place  of  meeting.  The 
Belgian  government  was  highly  favorable  to  the  plan.  It 
presented  to  the  representatives  of  all  nations  the  plan  of 
a  gathering  for  free  discussion,  requested  the  appointment 
of  delegates,  and  invited  numerous  statisticians  and  other 
scholars.  The  Statistical  Central  Commission  formed  the 
plans  for  the  meeting,  and  entrusted  their  execution  to  a 
committee  on  organization,  with  Quetelet  as  chairman. 
For  the  purposes  of  the  meeting  a  programme  containing 
the  questions  to  be  discussed  and  the  answers  of  the  ref- 
erees was  prepared,  and  a  division  into  sections  adopted. 
Rules  of  order,  containing  provisions  for  resolutions,  min- 
utes, the  language  to  be  used,  publication  of  proceedings 
and  papers,  etc.,  were  also  prepared. 

The  first  assembly  took  place  September  19,  1853.  The 
success  was  unexpected.  Repetitions  of  the  Congress  at 
intervals  were  generally  desired,  and  meetings  occurred 
in  1855  at  Paris,  in  1857  at  Vienna,  in  i860  at  London,  in 
1863  at  Berlin,  in  1866  at  Florence,  in  1869  at  the  Hague, 
in  1872  at  St.  Petersburg,  and  in  1876  at  Budapesth.     The 


History  of  Statistics.  79 

preparations  for  the  first  meeting  had  been  so  well  made 
that  the  permanent  organization  of  the  Congress  was 
effected  on  the  same  basis.  The  encouragement  of  the 
governments,  the  numerous  attendance,  and  the  dignified 
and  earnest  character  of  the  deliberations  were  features  of 
all  the  assemblies. 

In  1869  and  1872  it  was  decided  to  organize  a  Perma- 
nent Commission.  Its  duties  were  to  publish  the  resolu- 
tions of  the  Congress,  to  secure  information  as  to  their 
effect,  to  promote  the  possibility  of  comparison  in  the 
publications  of  the  various  states,  to  prepare  subjects  for 
discussion,  and  request  from  the  various  states  the  statis- 
tical material  necessary  for  their  investigation,  and,  finally, 
to  promote  comprehensive  international  statistical  investi- 
gations. Further  assemblies  were  frustrated  by  the  en- 
deavor to  make  this  commission  a  permanent  organ  in 
the  official  statistics  of  the  various  states,  and  the  failure 
to  see  that  the  practical  statistics  of  any  country  could  not 
be  determined  by  such  a  Congress. 

§48.    WORK   AND   INFLUENCE   OF  THE   CONGRESS. 

At  the  inauguration  of  the  Congress  Quetelet  defined 
its  purpose  as  follows :  The  deliberations  should  endeavor 
to  influence  the  statistical  work  of  the  various  states,  in 
order  to  increase  as  much  as  possible  the  facility  of  com- 
parison, and,  further,  to  bring  about  uniformity  in  the 
investigations  and  terminology. 

The  subsequent  attempt  to  establish  international  statis- 
tics met  with  little  success.  Even  the  simplest  problems 
proposed  (Population  by  Quetelet  and  Heuschling,  1865, 
and  Etat  de  la  Population  by  Berg,  1867)  showed  that  the 
obstacles  to  the  desired  completeness  and  comparability 
could  not  be  overcome  without  recourse  to  a  complicated 
system  of  hazardous  hypotheses.  The  investigations  which 
were  proposed  by  the  Congress  were  adopted  nowhere 
without  essential  changes  and  limitations.     It  would  have 


8o  Annals  of  the  American  Academy. 

been  impossible  for  the  Congress  to  determine  what  in 
each  particular  country  might  be  practicable.  Neverthe- 
less its  discussions  were  of  very  great  utility.  As  shown 
in  Appendix  II.,  the  discussions  of  the  Congress  touched 
nearly  every  single  problem  of  official  statistics.  As  a  rule, 
I  the  referee  for  each  problem  was  a  statistician,  from  the 
country  in  which  the  most  satisfactory  solution  of  the 
problem  had  been  given.  The  general  features  of  the 
problem  were  familiar  at  the  outset.  The  proposals  did 
not  touch  upon  them,  but  had  reference  to  the  details  of 
the  execution,  organization,  the  form  of  the  interrogatories, 
the  explanations  and  schedules.  The  proposals  might  per- 
haps go  too  far,  but  all  was  well  thought  out  and  carefully 
formulated  for  each  step  in  the  investigation.  This  was  a 
,  great  gain  for  the  comprehension  of  the  method.  The 
I  Congress  did  not  concern  itself  with  theory.  It  is  an 
I  exception  to  the  rule  when  a  resolution  of  1869  says: 
The  Congress  is  of  the  opinion  (1)  that  in  all  statistical 
researches  it  is  important  to  know  the  number  of  the 
observations  as  well  as  also  the  quality  or  nature  of  the 
facts  observed ;  (2)  that  in  a  series  of  large  numbers,  the 
qualitative  value  is  to  be  measured  by  the  divergences  of 
the  numbers  among  themselves  as  well  as  from  the  average 
of  the  series;  (3)  that  it  is  desirable  to  calculate  not  only 
the  averages,  but  also  the  oscillations,  in  order  to  know 
the  average  deviation  of  the  numbers  of  a  series  from  the 
average  of  the  series.  The  Congress  brought  to  the  mem- 
bers a  clear  conception  of  the  statistical  method,  and  com- 
plete agreement  in  regard  to  it.  The  entire  contents  of 
the  Compte-rendu  general  (the  last  St.  Petersburg,  1872) 
bear  testimony  to  this  point. 

Although  the  proposals  were  but  partially  applicable 
beyond  the  land  which  gave  them  birth,  they  furnished, 
nevertheless,  instructive  models,  and  served  to  spread 
similar  views  as  to  what  was  possible  and  useful  for  cer- 
tain purposes.  Certain  ideas  on  the  systematization  and 
improvement  of  the  investigations  were  accepted  as  a  mat- 


History  of  Statistics.  8i 

ter  of  course  by  the  large  number  of  statisticians,  and  were 
incorporated  in  the  statistics  of  all  countries,  even  in  those 
but  little  developed.  The  proceedings  and  dignified  repre- 
sentative character  of  the  Congress  increased  the  interest 
for  statistics  and  the  understanding  of  them  in  the  general 
public.  It  became  easier  for  the  governments  to  obtain 
the  means,  and  to  demand  from  the  officials  and  the  public 
things  which  could  not  have  been  thought  of  earlier.  In1 
a  brief  period  the  recognition  of  the  scientific  character  of 
statistics  and  the  necessary  extent  and  uniformity  of  its 
contents  has  been  greatly  extended.  Everything  which 
has  occurred  for  statistics  since  the  beginning  of  the  Con- 
gress has  been  essentially  a  consequence  of  its  stimulating 
and  invigorating  influence. 


II.  Modern  Statistical  Practice. 
§  49.  increased  need  of  statistics  and  statistical 

OFFICES. 

The  effects  of  the  Congress  were  however  based  also  on 
■the  needs  of  the  age. 

Since  the  movements  of  the  year  1848,  the  constitution 
and  administration  of  most  states  had  undergone  a  reor- 
ganization on  a  new  basis.  The  budgets,  and  the  business  I 
affairs  of  the  various  departments,  the  "  motifs  "  of  the 
laws,  and  the  discussions  of  the  legislative  bodies  required 
and  furnished  a  rich  statistical  material,  usually  with  an- 
nual repetitions.  This  increased  the  investigations  which 
had  been  the  subject  of  general  statistics  since  the  intro- 
duction of  the  statistical  bureaus. 

Numerous  private  institutions  began  to  feel  the  need  of 
statistics,  and  they  were  soon  indispensable.  Besides  life 
insurance  institutions  the  railway  companies  required  com- 
prehensive investigations  (Deutsche  Eisenbahn  Statistik,. 
yearly  since  1849;  Statistische  Nachrichten  iiber  die 
preussischen  Eisenbahnen,  since   1852,   etc.).     The  same 


82  Annals  of  the  American  Academy. 

is  true  of  the  credit  institutions  and  the  various  stock 
companies  required  by  law  to  publish  statements  and 
reports.  Reports  from  institutions  of  all  kinds,  founda- 
tions, and  societies  became  general  with  the  increased 
availability  of  printing  and  the  newspapers.  Thus  there 
accumulated  from  year  to  year  an  enormous  mass  of  ma- 
terial. As  soon  as  printed  it  could  be  referred  to,  often  in 
public  life,  and  hence  it  could  not  be  ignored  by  the  official 
statistics. 

States  which  up  to  this  time  had  possessed  no  statistical 
(bureaus  found  it  urgent  to  establish  them  on  the  model  of 
the  other  states.  Besides  those  named  in  §§  34-42,  statis- 
tical bureaus  were  founded  in  1853  in  Brunswick,  1858  in 
Gotha,  1859  in  Roumania,  1861  in  the  Argentine  Republic, 
and  in  1862  in  Servia.  In  1864  a  common  bureau  for  some 
of  the  Thuringian  States  (Weimar,  Altenburg,  Meiningen, 
the  two  principalities  of  Schwarzburg,  and  the  two  of  Reuss) 
was  established  at  Jena,  and  in  1865  bureaus  were  estab- 
lished in  Finland  and  Anhalt.  In  1869  Egypt,  1871 
Lubeck  and  Venezuela,  1872  Alsace  and  Lorraine,  1874 
Turkey,  and  1875  Japan  founded  statistical  bureaus.  The 
last  named  has  had  for  some  time  highly-developed  official 
statistics. 

A  number  of  Central  Commissions  are  also  to  be  men- 
tioned. Beside  those  already  noticed,  they  had  been 
organized  by  1 861  in  the  Electorate  of  Hesse,  Mecklen- 
burg-Schwerin,  Wurtemberg,  Hesse-Darmstadt,  and  Old- 
enburg. 

If  Since  1865  municipal  bureaus  have  been  created  in 
increasing  number.  Before  1870  they  had  been  founded 
pat  Berlin,  Leipzig,  Frankfort-on-the-Main,  Breslau,  Altona, 
Dresden,  and  outside  of  Germany  in  Vienna,  Buda-Pesth, 
Riga,  Venice,  Genoa,  Florence,  Rome,  and  Naples.  In 
1876  municipal  bureaus  existed  further  in  Chemnitz,  Stet- 
tin, Munster,  Prague,  Triest,  Brussels,  Copenhagen,  Milan, 
Messina,  and  Palermo. 


History  of  Statistics.  83 

§  50.  character  of  statistical  work. 

The   statistical    offices   assumed   at    this  time  in  their, 
administration,  still  more  however  in  their  work  and  the  1 
scope  of  their  labors,  a   uniformity  of  character  which,  \i 
considering  the  differences  of  the  nations,  was  truly  sur-  J 
prising. 

In  their  administration  the  offices  had  as  director  a  state 
official  directly  or  indirectly  dependent  on  the  Ministry, 
and  according  to  the  extent  of  the  work  specialist  asso- 
ciates, as  well  as  subordinate  officials  and  assistants  for 
the  clerical  operations.  Requests  and  directions  to  be 
transmitted  to  government  offices  were  required,  as  a  rule, 
to  pass  through  the  Ministry,  except  where  for  special 
purposes  direct  intercourse  was  permitted.  The  Provin- 
cial and  municipal  bureaus  are  subject  to  central  authority 
for  such  statistics  as  concern  the  whole  country,  but  inde- 
pendent for  their  own  particular  investigations. 

The  labors  of  the  bureaus  are  directed  chiefly  to  the 
compilation  of  the  numerical  material. 

Although  formerly  the  idea  prevailed  of  obtaining  in 
the  statistical  bureaus  organs  for  the  supervision  or  col- 
lection of  all  the  statistics  of  the  country,  the  field  of  the 
investigations  to  which  they  have  devoted  themselves  has 
become,  on  the  contrary,  comparatively  restricted.  It 
includes  generally  the  statistics  of  population  and  terri- 
tory ;  also  agricultural  statistics,  and  in  some  cases  also 
the  statistics  of  trade  and  commerce.  Apart  from  this 
they  were  generally  over-burdened  by  the  collection  of 
archives,  the  partial  publication  of  the  material  coming 
from  various  quarters,  and  by  the  replies  required  for  the 
numerous  questions  put  to  them  by  the  governments. 

For  all  their  publications  the  details  of  the  numbers    , 
occupied  unconditionally  the  foreground.     To  determine 
with  the  differences  of  time  and  locality  the  exact  results 
of  the    investigations,   and   to  preserve  them    for   future 
comparisons  and  problems  of  all  kinds  by  means  of  the 


84  Annals  of  the  American  Academy. 

printing  press,  must  be  admitted  to  be  a  much  more 
useful  and  necessary  application  of  time  and  money  than 
the  preparation  of  essays,  criticisms,  and  calculations,  in 
which  one  is  apt  to  lose  sight  of  the  basis  of  the  work,, 
as  the  form  of  presentation  will  not  admit  of  exhaustive 
explanations.  Besides  this,  it  is  to  be  considered  that  the 
criticism  of  the  correctness  of  this  basis,  of  the  method  of 
making  returns,  of  the  avoidance  and  removal  of  errors  by- 
means  of  more  stringent  requirements,  had  become  much 
more  strict,  and  that  in  consequence  the  labors  of  the  bu- 
reaus had  increased  accordingly.  This  was  the  reason  that 
in  the  course  of  time  the  publications  of  the  statistical 
institutions  were  limited  almost  exclusively  to  critically 
sifted  and  systematically  arranged  numerical  materials,  as 
complete  as  possible,  i.  e.,  essentially  to  the  comprehensive 
volumes  of  tables  which  pour  out  in  such  numbers  every 
year  from  all  civilized  nations. 

The  publications  consist  primarily  of  materials  (Quel- 
lenwerke)  which  give  the  material  detailed  in  tables,  and 
generally  only  the  most  necessary  combinations,  with  the 
directions  and  the  explanations  of  the  method  of  investi- 
gation; further  of  Annuals  (Jahrbucher),  which  give  short 
tabular  abstracts  of  the  main  results ;  and  finally  of  Peri- 
odicals (Zeitschriften),  which  are  open  to  the  essays  of 
private  investigators.  (The  long  list  of  such  publications 
from  the  various  states  can  be  best  found,  though  even  here 
not  quite  complete,  in  the  "  Katalog  der  Bibliothek  des 
Koniglichen  Statistischen  Bureaus  zu  Berlin,"  Vol.  I., 
1874,  II.,  1879,  and  the  more  recent  ones  in  the  "  Katalog^ 
der  Bibliothek  des  Deutschen  Reichstags,"  1882.) 

If  under  these  conditions  the  drawing  of  conclusions  as 
far  as  it  was  not  required  by  the  actual  needs  of  the  gov- 
ernment, was  mainly  left  to  private  persons,  scholars, 
legislators,  and  others,  it  could  not  but  follow  that  the 
stringency  of  the  method  should  become  an  object  of  the 
highest  interest  to  the  official  statistician.  The  need  and  the 
essence  of  stringent  critical  requirements  revealed  them- 


History  of  Statistics.  85 

selves  to  all  who  had  to  educate  a  number  of  subordinates 
in  making  uniform  observations.  It  was  felt  most  urgently, 
it  is  true,  by  the  central  orifices,  which,  like  the  Statistical 
Office  of  the  German  Empire,  were  obliged  to  formulate 
regulations  which  should  be  uniformly  understood  in 
numerous  and  greatly  differing  states,  and  which,  despite 
the  fact  that  the  freedom  in  the  execution  could  be  limited 
as  little  as  possible,  should  nevertheless  lead  to  homoge- 
neous results. 

On  the  basis  of  this  continuous  progress  and  stimulus 
to  the  methodical  procedure,  the  official  statisticians  came 
into  close  contact  with  the  statisticians  of  morals,  whose 
learned  researches  had  led  them  also  to  the  development 
of  the  critical  method. 


III.  The  Statisticians  of  Morals. 

§51.    IDEA    OF   CONSTRAINING    REGULARITY. 

The  more  official  statistics  were  limited  to  the  numeri- 
cal presentation  of  the  ascertained  facts,  and  the  more, 
therefore,  a  certain  dryness  in  the  treatment  and  the 
points  of  view  became  apparent,  the  more  the  statisti- 
cians who  sought  more  profound  contents,  and  results 
which  appealed  more  to  the  imagination,  turned  their 
attention  to  the  subject  of  social  physics,  as  Querelet  had 
named  it. 

Quetelet  left  no  doubt  that  he  was  convinced  of  the 
presence  of  laws,  capable  of  proof  by  calculation,  which 
govern  the  life  and  actions  of  man  and  society.  He  drew 
no  further  conclusions. 

Sir  F.  W.  Herschel,  the  astronomer  (born  1792,  died 
187 1),  drew  in  1850  the  more  definite  conclusion  that  the 
freedom  of  mankind  was  hardly  perceptible. 

H.  Thomas  Buckle  (born  1822,  died  1862)  declared  in 
his  "  History  of  Civilization  in  England,"  1857,  quite  can- 


86  Annals  of  the  American  Academy. 

didly  that  a  necessity  based  upon  natural  law  must  be  pre- 
supposed in  all  human  actions,  and  that  the  dogma  of  free 
will  must  be  totally  rejected.  With  this  consequential 
fatalism  he  hoped  to  place  all  historical  science  on  the 
basis  of  statistics. 

This  opinion  found  at  the  same  time  support  and  oppo- 
sition in  Adolf  Wagner's  "  Gesetzmassigkeit  in  den  schein- 
bar  willkiirlichen  Handlungen,"  1864;  support  in  the  strict 
deductions,  reaching  beyond  Quetelet's  material,  and  in  the 
manner  of  treating  large  numbers ;  opposition,  however,  in 
the  emphatic  rejection  of  every  deterministic  consequence, 
not  better  founded  but  more  distinctly  pronounced  than 
by  Quetelet. 

Other  and  particularly  Italian  statisticians  adhere  with 
preference  to  Quetelet's  idea  of  a  constraining  force  of 
natural  law  for  the  masses  and  freedom  for  the  individual. 
We  cite  Messedaglia,  Studii  sulla  populatione,  1866;  Cor- 
radi,  Hygiene  of  Italy;  Bodio,  Statistica  nei  rapporti  coll' 
economia  politica,  1869;  E.  Morpurgo,  Statistica  et  le  sci- 
enze  sociale,  1876  (German,  1877).  The  last  named  ex- 
presses the  general  opinion  in  holding  that  the  individual 
can  choose  freely  between  virtue  and  vice,  but  is  helpless 
in  face  of  the  laws  which  govern  the  masses,  and  that  the 
knowledge  of  these  laws  will  enable  statisticians  to  por- 
tray the  development  of  the  intellectual  and  moral  forces 
of  mankind,  and  the  ethical  order  of  the  universe  with 
the  same  precision  as  physics  explains  the  mechanism  of 
existence. 

§  52.    INCOMPATIBILITY   WITH    ETHICS   AND    PSYCHOLOGY. 

These  ideas  conflict  with  the  accepted  foundations  of 
ethics  and  psychology,  and  would  therefore,  should  they 
prove  correct,  lead  to  a  revolution  in  the  essential  princi- 
ples of  both  sciences.  The  representatives  of  the  latter 
have  very  generally  rejected  the  claims  of  these  ideas. 


History  of  Statistics.  87 

Some  works  attack  this  conception  of  the  statistics  of 
morals  from  an  ethical  or  psychological  standpoint. 

M.  W.  Drobisch,  "  Die  moralische  Statistik  und  die 
menschliche  Willensfreiheit,"  1867,  accuses  Wagner  of 
abandoning  the  doctrine  of  free  will,  and  allowing  it  to 
appear  that  the  idea  of  moral  responsibility  could  not  be 
supported. 

A.  v.  Oettingen,  "  Die  Moralstatistik  und  die  christ- 
liche  Sittenlehre,  Versuch  einer  Sozialethik  auf  empir- 
ischer  Grundlage,"  1868,  pronounces  Wagner  free  from 
fatalism,  but  does  not  approve  his  deductions.  In  oppo- 
sition to  Quetelet's  social  physics,  resting  on  a  naturalistic 
conception  of  the  universe,  and  also  to  the  common  theo- 
logical personal  ethics  resting  on  an  atomistic  spiritualism, 
he  endeavors  to  construct  a  theological  system  of  social 
ethics.  It  has  for  its  point  of  departure  that  unless  man- 
kind can  will,  state  and  church  would  be  senseless  and 
purposeless,  that  man  cannot  be  separated  entirely  from 
his  connection  with  the  human  community,  and  that  this 
constitutes  a  collective  body,  which  renders  it  improper 
for  the  individual  man  to  be  prompted  in  all  his  actions 
solely  by  egoism.      / 

A.  Heuermann,  "  Die  Bedeutung  der  Statistik  fur  die 
Ethik,"  1876,  has  maintained  that  it  is  ethically  valueless 
to  leave  merely  the  small  oscillations  in  the  great  num- 
bers to  the  freedom  of  the  will,  but  to  consider  the  law 
of  the  large  number  as  unconditionally  operative.  The 
law  of  causal  connection  requires  that  all  human  actions 
should  be  entirely  accounted  for.  It  does  not  exclude 
freedom,  but  rather  comprehends  it,  for  it  demands  that 
every  action  shall  be  the  comprehensible  product  of  a 
being,  weighing  the  motives  and  deciding  one  way  or 
the  other  without  compulsion. 


88  Annals  of  the  American  Academy. 

§53-  SOLUTION  OF  THE  PROBLExM   by  the  statistical 
METHOD. 

The  solution  of  the  problem  propounded  by  the  statis- 
ticians of  morals  has  been  most  effectively  given  by  statis- 
1  tics  themselves.  The  reasons  and  the  statistical  necessity 
•for  the  uniform  series  of  numbers  have  been  convincingly 
proved  to  be  totally  without  connection  with  any  com- 
pulsion of  the  free  moral  decision,  or,  indeed,  with  any 
limitation  whatsoever  of  the  will,  by  natural  law. 

G  Rumelin,  "Ueberden  Begriffeines  sozialen  Gesetzes," 
1867  (Reden  und  Aufsatze,  Vol.  I.),  had  already  denied 
that  a  constraining  necessity,  either  for  the  individual  or 
for  the  mass,  which  could  be  considered  a  law,  as  under- 
stood by  Buckle,  resulted  from  the  numerical  relations 
which  the  statisticians  of  morals  quote. 

G.  Schmoller,  "  Ueber  die  Resultate  der  Bevolkerungs- 
und'l^foralstaTistik,''  1871,  and  G.  F.  Knapp,  "  Die  neuen 
)  Ansichten  iiber  Moralstatistik,"  1871,  have  demonstrated 
!  more  in  detail,  and  quite  convincingly,  that  the  regular 
i  repetition   of  equally  large   effects   proves   nothing   more 
■  than  the  continuous  existence  of  equally  strong  causes, 
\  whether  they  be  internal  or  external.     And  further,  they 
show  that  this  regularity  which  is  explained  so  easily  and 
radically  by  the  assumption  of  natural  laws,  is  by  no  means 
so  constant  as  the  effect  of  physical  law.     The  regularity 
'  is  different  for  every  group  of  phenomena,  so  that  we  must 
have  for  each  group  a  particular  law,  and  for  the  whole  so 
intricate  a  complex  of  laws  that  the  result  has  a  remark- 
able similarity  with  that  which  follows  when  we  consider 
mankind  as  acting  according  to  inner  motives.     It  is  in 
fact  a  most  remarkable  predetermined  harmony,  that  ex- 
ternal   law  should   lead  men'  to  steal   wood  when  cold 
prevails,  and   bread  when  times   are  hard.     Therefore,  a 
constancy  of  certain  phenomena  of  moral  statistics  must 
be  considered  better  than  variations,  for  it  signifies  a  tri- 


History  of  Statistics.  89 

umph  of  the  moral  decision  of  the  will  over  tempting 
sensual  desires,  a  triumph  of  mind  over  matter. 

Chr.  Sigwart  in  "  Logik"  (1878,  Vol.  II.  p.  528)  declares 
further:  the  regularly  recurring  figures  express  nothing 
more  than  that  the  effects  which  show  that  the  causes 
present  in  individual  cases,  for  a  portion  of  the  community, 
are  equally  distributed  in  time.  This  result  of  an  equal 
distribution  in  time  would  be  most  expected  when  a  great 
number  of  causes  operating  independently,  variably,  and 
according  to  the  most  diverse  laws,  are  brought  to  bear 
upon  a  mass  of  objects,  uniform  in  number  and  composi- 
tion. It  is  just  the  accidental  nature  which  causes  us  to 
expect  the  equal  distribution,  and  we  should  seek  rather  a 
special  cause  in  perceiving  an  accumulation  of  such  events. 
The  regularity  of  the  numbers  permits  a  conclusion  that 
the  conditions  are  constant. 

All  these  considerations  as  to  the  nature  of  the  regular 
phenomena  of  the  statistics  of  morals,  which  place  the 
question  in  the  proper  scientific  light,  presuppose  a  cor- 
respondingly profound  penetration  into  the  comprehension 
of  the  statistical  method. 

IV    Conceptions  of  Statistical  Theory. 

§  54.    OPPOSING    POSITIONS. 

The  question  of  statistical  theory,  is  closely  allied  to 
that  of  the  essence  of  statistics  as  a  science,  that  of  its 
sphere  as  a  portion  of  human  knowledge,  and  that  of  its 
specific  contents  whereby  the  limits  of  this  knowledge  are 
extended.  These  fundamental  ideas,  which  either  help- 
fully or  misleadingly  influence  the  theory,  have  been  sel- 
dom, however,  discussed  in  connection.  But  few  specifically 
theoretical  treatises  of  a  comprehensive  character  can  be 
mentioned.  The  conception  of  each  statistician  appears 
most  clearly  in  his  definition  of  the  subject.  Most  of 
them,  however,  simply  pronounce  such  a  definition  as  an 


go  Annals  of  the  American  Academy. 

introduction  to  the  subject,  with  scarcely  an  endeavor  to 
make  the  definition  the  fundamental  idea  and  crowning 
point  of  a  detailed  system. 

In  these  definitions  we  find  essentially  the  old  opposing 
views  of  the  statistics  of  the  state  and  those  of  population. 
The  idea  of  a  distinct  method  of  investigation  is  a  new 
feature  which  begins  to  make  itself  felt  in  the  discussion. 

Every  scientific  treatment  must  either  place  in  the  fore- 
ground the  object  or  else  attach  itself  to  the  method  of  the 
investigation.  In  the  first  instance  no  mode  of  investiga- 
tion maybe  neglected  in  order  to  gain  a  systematic  knowl- 
edge of  the  object.  If  the  state  is  to  be  the  subject  of  the 
science,  it  would  obviously  be  a  one-sided,  arbitrary  limita- 
tion, to  consider  it  only  from  the  results  of  enumerations. 
In  the  second  case  the  more  a  particular  process  is  matured, 
and  the  more  critical  its  applications  the  more  numerous 
and  diverse  are  the  objects  which  are  accessible  to  it. 
There  may  result  such  a  general  connection  of  the  prin- 
ciples that  a  systematic  knowledge  of  the  method  will  be 
possible.  The  opposing  opinions  of  statistical  theorists 
oscillate  between  these  two  possibilities. 

§55.  conception  in  the  sense  of  statistics  of 
the  state. 

In  their  adherence  to  the  object  simply,  without  consid- 
eration of  the  method  used  to  obtain  their  knowledge  of  it, 
Achenwall's  school  weremostpersistent.  To  obtain  "Staats- 
kunde,  Staatsbesonderheiten,  and  Staatenvergleichungen  " 
(political  descriptions,  phenomena,  and  comparisons  of 
states)  in  such  a  form  as  should  exhaust  as  far  as  possible 
everything  worth  knowing  was  Achenwall's  aim.  The 
method  by  which  this  information  should  be  gained  was 
of  little  consequence.  The  so-called  theoretical  essays  of 
1  the  school  treat  rarely  of  anything  beyond  the  manner 
of  grouping  facts  and  a  few  principles  for  comparisons. 

One  can  no  longer  speak  of  a  school  of  Achenwall,  yet 


History  of  Statistics.  9r 

there  are  quite  a  number  of  statisticians  who  in  theory  \ 
remain  true  to  its  traditions. 

J.  E.  Wappaus  (born  18 1 2,  died  1879)  in  "  Bevolkerungs- 
statistik,"  1859,  and  Robert  v.  Mohl  (born  1799,  died  1875), 
in  "  Geschichte  und  Literatur  der  Staatswissenchaften " 
(1858,  Vol.  III.  p.  647),  express  the  same  opinion  that  if 
statistics  is  not  to  lose  its  character  as  a  science,  it  must 
adhere  in  essence  to  the  definition  of  Achenwall,  that  it  is 
by  no  means  limited  to  such  facts  and  conditions  as  can 
be  expressed  in  numbers,  but  must  rather  reflect  in  an 
exhaustive  manner  all  actual  and  social  conditions  of  the 
population. 

Lorenz  v.  Stein,  "System  der  Staatswissenschaften" 
(1852,  Vol.  I.  p.  83),  finds  Schlozer's  definition  appro- 
priate: "Statistics  is  stationary  history." 

Also  A.  Gaillard,  "  Elements  de  statistique  humaine  ou 
demographie  comparee  "  (1855);  Jonak,  "Theorie  der  Sta- 
tistik  "  (1856);  and,  similarly,  Zuccagni-Orlandini,  Iginio, 
Zambetti,  and  Nardi  consider  the  physical,  economic, 
political,  and  moral  conditions  of  the  state  as  the  subject 
of  the  data  and  research  of  statistics. 

The  underlying  ideas  of  the  Austrian  "  Prufungs  regle- 
ment"  of  July  29,  1850,  and  the  rescript  appointing  the 
Prussian  Central  Commission  of  July  9,  i860,  correspond 
also  to  this  point  of  view. 

Further,  it  cannot  be  overlooked  that  though  the  Inter- 
national Statistical  Congress  was  thoroughly  convinced 
that  statistical  information  is  entirely  dependent  on  me- 
I  thodical,  exact,  numerical  investigations,  yet,  nevertheless, 
that  its  whole  system  coincided  very  closely  with  Achen- 
wall's  statistics,  and  that  it  gave  support  to  the  idea  that 
an  examination  of  the  life  of  states  and  peoples,  and 
a  comparative  description  of  states,  were  to  be  understood 
as  statistics.  Indeed,  the  Congress  says  expressly  in  the 
Report  of  1853,  "without  doubt  statistics  operates  with 
numbers,  numbers  are  its  chief  element,  but  they  are  not 


v4 


92  Annals  of  the  American  Academy. 

the  only  one,  statistics  is  also  *  la  science  raisonnee  des 
felts.' " 

Finally,  this  conception  finds  support  in  a  great  number 
of  literary  works,  which,  as  W.  Roscher,  in  "  Geschichte 
der  Nationalokonomie  in  Deutschland "  (1874,  p.  ion), 
expressly  says,  cannot  properly  be  classed  elsewhere  than 
under  statistics.  He  mentions  :  Wappaus,  Amerika  (1855) ; 
v.  Viebahn,  Zollvereintes  Deutschland  (1858);  Bavaria 
(i860);  Meitzen,  Der  Boden  des  Preussischen  Staates 
(1868).  He  could  have  added  "Das  Konigreich  Wurt- 
temberg"  (1863);  Wirth,  Schweiz  (1871);  Ratzel,  Ver- 
einigte  Staaten  (1878);  "Das  Grossherzogthum  Baden" 
(1885),  and  others.  His  reference  to  W.  Riehl's  "  Natur- 
geschichte  des  Volkes"  shows,  on  the  other  hand,  the 
obvious  necessity  of  separating  from  statistics  the  descrip- 
tion of  countries  as  an  independent  scientific  department. 

§  56.  conception  as  science  of  human  communities. 

Though  the  metaphysical  flights  of  the  statisticians  of 
morals  must  be  considered  as  too  ambitious,  and  their 
explanation  of  facts  as  a  deviation  from  true  principles  of 
science,  yet  a  large  number  of  professional  statisticians 
adhere  to  the  same  field  of  research  as  the  essential  one 
of  their  science.  That  is  to  say,  the  penetration  into  the 
condition  and  changes  of  the  social  life  of  mankind,  the 
observation  of  the  so-called  human  communities  (Gemein- 
schaften)  appears  to  them  as  the  scientific  object  of  sta- 
tistics. What  Quetelet  and  his  followers  looked  upon  as 
constraining  laws,  this  more  realistic  school  in  statistics 
regards  as  a  sphere  of  regularities  which  lead  to  the  dis- 
covery and  explanation  of  similar  conditions  and  causes. 
Two  decades  after  Moreau  de  Jonnes  (§  46)  this  idea  be- 
came very  general. 

F.  B.  W.  v.  Hermann  (§  34)  (Die  Bewegung  der  Bevolk- 
erung  in  Bayern,  1863)  says  :  Everything  in  the  activity  of 
the  state  and  the  life  of  the  people  which  can  be  reduced 


History  of  Statistics.  93 

to  size  and  number,  and  be  quantitatively  compared,  be- 
comes the  object  of  statistics. 

Bruno  Hildebrand,  in  the  essay  "  Die  wissenschaftliche 
Aufgaben  der  Statistik  "  (Jahrbuch  fur  Nationalokonomie 
und  Statistik,  Vol.  I.,  1866)  writes:  Statistics  notes  all 
similar  actions  and  experiences  of  men  in  a  given  space, 
and  calculates  the  relation  of  the  total  of  these  phe- 
nomena to  the  total  number  of  men,  or  of  actions  and 
experiences,  in  the  same  time  and  locality,  and  thus  finds 
relative  numbers  which  express  as  unimpeachable  gen- 
eral facts  the  rules  which  govern  the  occurrence  of  the 
individual  actions  and  experiences. 

A.  Frantz  (Handbuch  der  Statistik,  1864),  Rameri  (1869), 
de  Luca,  and  Racioppi  agree  with  this  conception.  W. 
Lexis  (Theorie  der  Massenerscheinungen,  1877)  expresses 
the  same  thought  as  follows  :  Statistics  have  the  inde- 
pendent problem  of  considering  and  investigating  accord- 
ing to  exact  methods  the  characteristic  collective  phe- 
nomena of  human  life  which  are  accessible  to  scientific 
observation.  The  enumeration  of  all  individual  cases  of 
the  phenomenon  forms  the  basis  of  its  method. 

G.  Mayr  (Gesetzmassigkeit  im  Gesellschaftsleben,  1877, 
p.  13)  distinguishes  between  the  statistical  method  and  the 
narrower  sphere  of  statistics  as  an  independent  science. 
The  application  of  the  statistical  method  is  not  confined 
to  the  life  of  society,  but  is  used  also  in  the  observation 
and  study  of  purely  natural  facts.  But  the  observation  of 
the  purely  natural  facts  which  have  no  connection  what- 
ever with  the  social  life  of  mankind,  must  be  excluded 
from  the  sphere  of  the  independent  science  of  statistics. 
He  defines  statistical  science  as  the  systematic  presenta- 
tion and  exposition  of  the  actual  occurrences  of  social  life 
and  the  laws  resulting  therefrom,  upon  the  basis  of  the 
quantitative  observation  of  aggregates. 

Quite  in  accord  with  these  views  are  M.  Block  (Traite 
theorique  et  pratique  de  statistique,  1878,  1886)  and  Th.  v. 
Inama-Sternegg  (Statistische  Monatshefte,  Wien,  1882). 


94  Annals  of  the  American  Academy. 

E.  Engel  (§  34),  to  whom  particular  merit  in  the  forma- 
tion of  the  theory  and  practice  of  statistics  is  justly- 
accorded,  declares  statistics  to  be  a  science,  to  which  he 
gives  the  name  of  demology  or  the  science  of  human 
\Zcommunities.  Its  aim  is  to  observe  in  its  phenomena  the 
physical,  intellectual,  and  moral  life  of  the  peoples  of 
organized  states,  to  formulate  its  observations  arithmeti- 
cally, and  to  demonstrate,  as  it  were,  by  analysis  the  con- 
nection of  cause  and  effect  in  these  phenomena.  Its  field 
of  observation  is  not  individuals  but  aggregates  united 
and  grouped  into  communities,  on  the  one  hand,  of  families, 
clans,  tribes,  nations,  and  peoples,  and,  on  the  other,  in 
classes  of  rank,  wealth,  occupation,  faith,  and  so  forth.  It 
becomes  the  physics  and  physiology  of  society,  and  forms, 
as  it  were,  a  link  between  the  social  and  natural  sciences. 
Besides  the  physiological,  positive,  comparative,  and  prag- 
matic demology,  which  he  further  divides  according  to 
particular  modes  of  treatment,  he  considers  also  practical 
demology  or  the  method  of  statistics,  which  includes  its 
methods  and  resources,  its  applications,  its  workshops,  its 
aims,  and  its  achievements. 

Upon  this  conception  of  the  scientific  sphere  of  statis- 
tics a  great  number  of  acute,  penetrating  works  on  method 
have  appeared,  which  though  they  treat  only  of  special 
phases  of  the  statistics  of  population,  are  capable,  never- 
theless, of  casting  a  bright  light  on  every  kind  of  statis- 
tical investigation. 

E.  Engel,  Methode  der  Volkszahlungen,  1861;  Fabri- 
cius,  Zur  Theorie  und  Praxis  der  Volkszahlungen,  1868; 
M.  M.  v.  Baumhauer,  Bevolking  in  1863  (Statistisch  Jaar- 
boekv.  h.koningrijk  der  Nederlanden,Vol.i4,  Part  I.,  1867). 
Wittstein,  Mathematische  Statistik  in  ihrer  Anwendung, 
1867;  Zeuner,  Abhandlungen  aus  der  mathematischen 
Statistik,  1869;  G.  F.  Knapp,  Ueber  die  Ermittelung  der 
Sterblichkeit,  1868,  and  Theorie  des  Bevolkerungswech- 
sels,  1874;  K.Becker,  Zur  Berechung  von  Sterbetafeln, 
1874,   and    Bericht    von    July    10,     1874   (Statistik    des 


Jf 


History  of  Statistics.  95 

Deutschen  Reiches,  Vol.  XX.,  I.,  p.  145);  R.  Boeckh,  Ster- 
ol ichkeitstafel  fur  den  preussischen  Staat,  im  Umfange  vor 
1865,  1875  ;  W.  Lexis,  Einleitung  in  die  Theorie  der  Bevol- 
kerungsstatistik,  1875,  and  Theorie  der  Massenerscheinun- 
gen  in  der  menschlichen  Gesellschaft,  1877. 

§  57.    CONCEPTION   OF   STATISTICS   AS   A   SCIENCE   OF 
,  METHOD. 


b 


Opposed  to  this  numerous  list  of  statisticians  who  regard 
k  the  distinctively  numerical  method  proper  for  statistical 
practice,  but  find  the  theoretical  essence  of  statistics  in  the 
idea  that  it  has  for  its  subjects  the  life  of  states  and  peo- 
ples, or  of  human  communities,  there  is  another  group  of 
^statisticians  who  consider  this  object,  the  life  of  mankind, 
to  be,  though  prominent,  merely  accidental,  the  result  of 
circumstances,  or  not  exclusive  of  other  things,  and  who  on 
the  contrary  find  the  scientific  character  of  statistics  in  the 
method  itself.  This  view  was  pronounced  by  Potlock  and 
Cournot  (§  46).  "" 

Riimelin  (Zur  Theorie  der  Statistik,  Tiibinger  Zeitschrift, 
1863)  treats  it  with  great  penetration.  He  sees  in  statis- 
tics proper  a  methodical  auxiliary  science,  which  he  com- 
pares to  other  auxiliary  sciences,  which,  like  philosophical 
critique  and  hermeneutics,  consist  merely  in  the  exercise 
of  formal  and  methodical  processes.  His  conception  is 
based  on  the  nature  of  the  phenomena  capable  of  enumera- 
tion, in  their  relation  to  those  numerically  fixed  or  typical. 
In  nature,  as  he  says,  the  individual  is  typical,  hence  a 
single  accurately  ascertained  fact  justifies  an  induction. 
Logic  puts  together  only  the  constant  qualities  as  making 
up  the  idea,  but  cannot  turn  to  account  scientifically  that, 
which  in  one  case  occurs  so,  in  another  differently,  in  a 
word,  the  variable  factors.  The  statistical  method  enters 
in  the  empirical  sciences  just  at  the  point  where  induction, 
the  conclusion  from  the  single  typical  case  to  other  cases, 
is  not  available.     Briefly,  the  statistical  procedure  may  be  ^ 


g6  Annals  of  the  American  Academy. 

called  the  methodical  observation  of  aggregates.  It  con- 
sists in  spreading,  as  it  were,  a  network  of  observations 
over  entire  groups  of  individuals,  in  order  to  observe  and 
register  by  a  single  method  all  phenomena  of  the  same 
class.  This  method  of  observation  dissolves  the  collec- 
tive ideas  of  race,  church,  district,  rank,  and  others  into 
the  individuals  which  compose  them,  in  order  to  observe 
for  each  individual  whether  in  his  case  a  certain  phe- 
nomena occurs  or  not.  It  is,  therefore,  clear  that  it  is 
always  concerned  with  an  enumeration,  and  that  the  num- 
ber is  typical  of  this  method  of  observation.  The  more 
numerous  the  objects  of  such  observation,  the  more  ex- 
tended the  single  groups,  and  the  more  numerous  the 
groups  subjected  to  the  same  observation  the  more  com- 
plete and  thorough  does  the  characterization  of  the  col- 
lective idea  become,  and  the  richer  becomes  the  material 
for  inductive  reasoning  and  for  the  knowledge  of  the  in- 
terdependence of  human  phenomena.  Thus  a  way  is 
obtained  to  characterize  correctly  collective  ideas. 

4dolf  Wagner  (§  5  1.  Article  Statistik  in  Bluntschli  und 
Brater,  Staatsworterbuch,  1867)  characterizes  the  general 
idea  of  statistics  as  the  methodical  inductive  procedure  for 
the  solution  and  explanation  of  the  mechanism  of  human- 
ity and  nature,  of  the  real  world  generally,  i.  e.,  for  the 
derivation  and  explanation  of  the  laws  according  to  which 
the  mechanism  acts,  and  for  the  discovery  and  explanation 
of  the  causal  connection  between  the  individual  human  and 
natural  phenomena,  by  means  of  a  system  of  methodical 
observations  of  the  aggregates  of  these  phenomena,  lead- 
ing to  a  determination  of  their  quantitative  relations. 

M.  Haushofer  (Lehr-  und  Handbuch  der  Statistik,  1872) 
designates  statistics  as  an  essentially  methodical  science. 
He  says  statistics  is  a  method  and  a  science.  Conceived 
as  systematic  investigation  of  aggregates  it  is  a  method. 
To  be  a  science  there  must  be  beyond  the  unity  of  the 
method  a  certain  unity  of  the  object.  This  object  is  the 
aggregate  of  phenomena  as  such.     Statistics  is,  therefore, 


History  of  Statistics.  97 

the  science  of  aggregate,  and  in  particular  of  the  aggre- 
gate of  human  and  political  phenomena,  of  their  move- 
ment, and  its  laws.  Statistics  is  for  him,  nevertheless, 
merely  an  auxiliary  science.  It  seeks  and  finds  truth,  but 
only  such  truth  as  is  utilized  by  other  sciences.  Its  char- 
acter as  method  is  therefore  predominant. 

The  idea  that  the  scientific  essence  of  statistics  was  not  to 
be  sought  in  a  specific  object,  but  in  the  manner  according 
to  which  any  object  in  its  multiplicity  is  investigated,  is 
found  accordingly  in  certain  works  which  treat  of  special 
problems  as  examples  of  methodical  procedure:  G.  Mayr, 
Ueber  die  Grenzen  der  Vergleichbarkeit  statisticher  Daten, 
1866 ;  and  Ueber  die  Anwendung  der  graphischen  Methode, 
1877  ;  Die  Aerzte  und  das  medizinische  Hulfspersonal  (Sta- 
tistik  des  Deutschen  Reiches,  Vol.  XXV.,  1877);  G.  Tam- 
meo,  Le  medie  et  loro  limiti,  1878;  Marey,  La  methode 
graphique  dans  les  sciences  experimentales,  1879;  Perozzo, 
on  the  graphical  representation  of  successive  entireties 
with  three  coordinates  (Annali  di  statistica,  Ser.  II.,  Vol. 
XIV.,  1880). 

The  application  of  the  statistical  method  to  phenomena 
which  are  totally  distinct  from,  or  else  only  remotely  con- 

ected  with,  political  and  social  life,  or,  as  it  has  been'?  / 
called,  "demography,"  has  done  much  to  confirm  the  view 
of  the  scientific  character  of  statistics  which  we  are  con- 
sidering. 

Meteorology,  particularly  from  the  standpoint  of  telluric 
and  cosmic  physics,  exceeds  in  the  precision  of  the  statis- 
tical observations  and  conclusions  every  other  field  of  sta- 
tistics.    Botany  and  zoology  have  besides  the  history  also 
statistics  of  their   living   and  fossil   genera  and  species. 
I  Astronomy  has  based  upon  the  consequences  of  Herschel's 
f  system  exact  statistics  of  the  stars  in  their  order  of  mag- 
I   nitude.      Medicine  applies  the   statistical   method  in  the 
broadest  sense  for  the  comparative  judgment  of  the  phe- 
nomena of  sickness  and  health.  Even  philology  has  profited 


■  1 
u 


98  Annals  of  the  American  Academy. 

from  the  statistical  treatment  of  the  recurrence  of  words 
and  sounds. 

M.  Block  (§  56)  declared  as  early  as  i860  (Statistique  de 
la  France)  all  such  applications  of  the  method  to  be  sta- 
tistics. Rumelin  wrote,  1874:  "The  statistical  method 
takes  hold  everywhere,  where  it  finds  variable  factors  in 
the  phenomena  brought  under  its  observation.  And  these 
exist  everywhere  and  in  all  the  realms  of  nature.  Some 
interest  may  attach  itself  in  every  case  to  these  variable 
elements.  It  could  possibly  be  deemed  worth  while  to 
sort  grains  of  sand  according  to  size  and  count  them." 
(This  actually  takes  place  with  great  accuracy  in  recent 
investigations  of  soils.)  "  It  is  at  present  not  to  be  fore- 
seen what  significance  the  method  may  attain  in  the  vari- 
ous fields  of  natural  science.  Up  to  the  present  moment 
it  finds  extensive  and  steadily  increasing  employment  in  a 
number  of  them,  in  meteorology,  in  physiology,  and  in 
medicine." 

§  58.  conception  of  statistics  as  applied  logic. 

From  the  recognition  of  the  idea  that  the  scientific  char- 
acter of  statistics  was  its  peculiar  method,  irrespective  of 
the  object  to  which  it  might  be  applied,  it  was  an  easy  step 
to  the  conception  of  the  method  as  a  branch  of  logic,  as  an 
extension  of  the  logical  mental  processes,  and  with  a  cer- 
tain scientific  independence. 

A  similar  general  character  has  been  ascribed  to  statis- 
tics by  John  Stuart  Mill  in  his  ".System  of  deductive  and 
inductive  logic,"  1843.  He  treats  of  the  methods  of  proba- 
bilities and  of  comparison  in  the  same  spirit.  Caporale 
also  said  in  his  Lezioni,  1863,  "statistics  is  logic,  numerical 
analysis,  and  synthesis  of  facts,  presented  in  tables  for 
definite  useful  purposes," 

Christoph  Sigwart  in  "Logik"  (Vol.  I.,  1873,  II.,  1878) 
gives  the  subject  the  first  exhaustive  treatment.  He  begins 
with  the  proposition  that  the  general  purposes  of  thought 


History  of  Statistics.  99 

demand  of  human  perception  that  it  should  describe  ob- 
jectively, exhaustively,  and  accurately  the  single  things 
and  occurrences  which  present  themselves,  and  class  them 
according  to  time  and  species.  This  completeness  of  human 
perception  in  time  and  space  could,  as  he  says,  be  repre- 
sented only  by  a  description  of  the  world,  comprising  all 
perceptible  things  in  their  order  of  time  and  space,  a  spe- 
cies of  universal  catalogue  of  all  single  objects  and  their 
changes.  Uranography  and  geography  are  already  far 
advanced  in  the  discovery  of  things  and  their  designation 
with  proper  names.  As  far  as  such  completeness  of  de- 
scription is  not  possible  it  is  supplemented  by  the  statistical 
enumeration  of  similar  things  and  occurrences  under  the 
assumption  of  an  existing  classification  of  the  objects.  As 
far  as  the  classification  of  form  and  matter  proceeds  accord- 
ing to  perceptible  qualities,  every  description  of  a  single 
object  serves  to  include  it  among  the  classes  already 
formed,  or  else  to  extend  the  sphere  of  the  latter. 
Thus  it  is  discovered  what  single  objects  belong  to 
one  and  the  same  class,  and  this  leads  to  ascertaining 
how  many  similar  objects  exist,  in  short,  to  their  enu- 
meration. In  this  enumeration  the  individual  thing  is 
lost — it  becomes  one  of  a  group  of  similar  units.  The 
common  designation  of  this  species  of  cataloguing  by 
rubrics  the  number  of  single  objects  included  under  a 
general  idea,  is  statistical  returns  or  tables.  The  main 
characteristic  of  statistical  returns  consists  in  the  fact  that 
1  the  single  objects  are  not  enumerated  and  catalogued  as 
uch,  but  that  they  furnish  totals  of  similar  objects  and 
phenomena,  thus  summarizing  the  individual  perceptions 
in  distinct  rubrics.  Enumeration  has  special  importance 
as  a  means  of  describing  aggregates  whose  constituent 
elements  are  either  all  similar  or  else  included  under  a 
limited  number  of  general  ideas.  This  description  or 
characterization  of  aggregates  is  the  primary  aim  of 
^statistics.  The  next  step  in  the  use  of  the  results  obtained 
by  enumeration  is  the  presentation  of  the  relations  existing 


ioo  Annals  of  the  American  Academy. 

between  the  numbers  in  the  most  easily  observed  form. 
It  replaces  the  various  totals,  which  as  such  afford  little 
insight  into  the  subject,  by  average  values,  in  order  to 
have  a  measure  of  their  size,  a  means  of  comparison  with 
others.  Its  purpose  is  to  establish  a  permanent  measure, 
a  rule.  The  averages  show  empirical  regularities,  descrip- 
tive in  their  nature  and  incapable  of  expressing  a  necessity 
without  the  aid  of  the  assumption  that  the  occurrences 
which  produce  the  individual  varying  instances  in  a  certain 
field  are  constant  in  their  totality.  A  rule  can  only  be 
assumed  when  the  average  of  a  large  field  repeats  itself 
uniformly  in  the  smaller  fields  which  go  to  make  up  the 
whole.  The  statistical  conclusion  on  causality  can  be  based 
|  only  on  the  variations  and  not  on  the  constancy  of  the 
s  numbers.  The  deviation  from  the  average  is  an  indication 
that  the  features  distinguishing  a  part  from  the  whole 
cause  the  differences  in  the  number  of  the  phenomena  of 
that  part.  Statistics  show  that  causes  known  from  other 
sources  have  had  their  effects,  that  they  have  not  been 
neutralized  by  others,  and  give  thus  a  measure  of  the 
intensity  of  each  force  in  relation  to  all  the  others.  But 
it  is  impossible  for  statistics  to  be  an  expression  of  a  ruling 
necessity  in  the  single  cases  enumerated.  In  as  far  as  we 
are  able  to  reduce  the  individual  occurrence  to  actual  laws, 
enumerations  of  the  objects  is  the  only  way  of  obtaining 
satisfactory  information  concerning  certain  phenomena 
presented  to  our  intelligence.  As  soon  as  laws  are  found, 
which  can  only  be  hoped  for  by  means  of  analysis  and 
the  application  of  inductive  methods,  the  statistical  enu- 
meration ceases  to  be  of  interest. 


supplement  to  the 
Annals  of  the  American  Academy  of  Political  and  Social  Science, 

May,  1891. 


HISTORY, THEORY,  AND  TECHNIQUE 


OF 


STATISTICS. 


BY 
AUGUST  MEITZEN,  Ph.D., 

PROFESSOR   AT  THE   UNIVERSITY  OF   BERLIN. 


TRANSLATED,  WITH  AN   INTRODUCTION, 

BY 
ROLAND  P.  FALKNER,  Ph.D., 

INSTRUCTOR  OF   STATISTICS,  UNIVERSITY  OF  PENNSYLVANIA. 


PART    SECOND: 
THEORY  AND  TECHNIQUE  OF  STATISTICS. 


PHILADELPHIA: 

AMERICAN  ACADEMY  OF  POLITICAL  AND  SOCIAL  SCIENCE. 

189I. 


PART  II. 

THEORY  AND  TECHNIQUE  OF  STATISTICS. 


INTRODUCTION. 
§59.    POSITION   OF   STATISTICS   AS   A   SCIENCE. 

That  statistics  has  long  since  attained  the  importance 
and  general  recognition  of  a  science  is  shown  by  the  his- 
tory of  its  development.  This  history  also  demonstrates 
the  complete  unanimity  which  exists  in  regard  to  the  pur- 
pose and  processes  of  the  statistical  method.  None  the  less 
the  scientific  character  of  statistics,  and  its  position  in  the 
general  system  of  sciences,  have  remained  a  matter  of 
controversy. 

A  conflict  of  opinion  still  exists  on  the  question,  whether 
statistics  is  to  be  considered  as  a  science  of  things  or  a 
science  of  method. 

One  group  of  statisticians  considers  statistics  as  a  sci- 
ence to  be  wholly  independent  of  any  distinct  method,  but 
as  attached  to  certain  objects,  constituting  our  scientific 
knowledge  of  them.  These  investigators  either  hold  fast 
to  the  opinion  that  the  knowledge  of  the  State,  con- 
ceived somewhat  as  Achenwall  formulated  it,  is  the  only 
true  and  valuable  object  of  statistics  as  a  science,  or,  with 
Sussmilch,  they  consider  the  reign  of  law  in  the  phe- 
nomena of  human  existence,  in  the  physiological  and 
moral  occurrences  of  the  life  of  nations,  as  the  peculiar 
content  of  statistical  inquiry. 

Another  group  recognizes  the  importance  of  the  statis- 

(103) 


104  Annals  of  the  American  Academy. 

tical  method  as  such,  and  finds  in  its  application  to  the 
conditions  of  nations  and  peoples  or  human  communities 
the  field  of  scientific  statistical  knowledge. 

A  third  party  finally  declares  statistics  to  be  exclusively 
a  science  of  method,  applicable  to  every  object — to  be 
applied  logic,  and  to  be  classed  with  other  independent 
methodological  sciences,  such  as  logic,  mathematics,  cri- 
tique, and  hermeneutics. 

It  must  be  clear  that  the  questions,  whether  statistics  is 
a  science,  and  if  so,  what  is  its  place  in  the  general  system 
of  sciences,  cannot  be  decided  upon  the  basis  of  statistics 
itself.  To  bring  into  clear  relief  the  many  related  ideas 
and  manifold  actual  connections  of  thought,  and  assign  to 
every  field  of  investigation  its  proper  place,  would  require  a 
comprehensive  analysis  of  all  human  knowledge,  a  general 
theory  of  science. 

The  lack  of  such  a  standard  for  the  sciences,  which  on 
account  of  the  necessity  of  metaphysical  premises,  must, 
in  any  case,  receive  a  coloring  from  the  individual  tem- 
perament, makes  itself  very  keenly  felt  in  the  development 
of  the  system  of  statistics.  A  clear  definition  of  the  sphere 
of  ideas  to  be  considered  is  demanded  not  only  for  the 
elegance  of  the  treatment,  but  as  an  almost  indispensable 
proof  of  a  clear  and  precise  system  of  ideas. 

Statistics  is  therefore  called  upon  all  the  more  urgently  to 
form  its  own  ideas  into  a  sound  theoretical  system,  taking 
into  account  all  particulars  and  details. 

§  60.    POINTS   OF   VIEW   FOR  THE   THEORY   OF  STATISTICS. 

Obviously  the  theory  of  statistics  cannot  treat  of  the 
\  J  actual  situation  of  innumerable  phenomena,  which  have  so 
long  been  ascertained  in  civilized  countries,  and  which 
vary  as  they  do  from  year  to  year.  How  many  inhabitants 
there  may  have  been  in  Rome  at  a  certain  period,  how 
great  the  public  debt  of  Spain,  how  extensive  the  railroad 
traffic  in  Russia,  etc.,  are  facts  of  interest  merely  for  the 


Theory  and  Technique  of  Statistics.  105 

description  or  history  of  Rome,  Spain,  and  Russia.  And 
if  on  the  average  21  boys  are  born  for  every  20  girls,  it 
is  not  for  statistics  but  for  anthropology  to  examine 
whether  this  statistical  probability  can  or  must  be  ac- 
cepted as  final.  Even  in  the  most  exclusive  circle  of  Achen- 
wall's  school,  the  theory  of  statistics  treats  of  the  system 
and  not  of  the  contents  of  the  "  Staatsmerkwiirdigkeiten." 
The  problems  which  practical  and  theoretical  statisticians 
are  called  upon  to  solve  are  part  of  the  theory  of  statistics, 
not  with  reference  to  their  anthropological,  geographical, 
political,  or  economic  importance,  but  as  the  subjects  of  dif-h 
ferent  varieties  of  investigation.  Each  case  is  for  {he  »\ 
theory  an  illustration  or  a  problem. 

The  theoretical  point  of  view  must  necessarily  be  con- 
cerned with  the  propriety  and  practicability  of  the  plan  of 
observation,  the  manner  of  execution,  the  reliability  and 
utility  of  the  results,  the  combination  of  the  facts,  and  the 
correctness  of  the  conclusions.  These  are  all  questions  of 
method.  For  all  these  phases  the  theory  needs  authorita- 
tive principles,  an  understanding  of  the  relations,  and  the 
means  for  facilitating  an  examination  and  judgment  of 
them.  \ 

The  theory  of  statistics  must  therefore  be  based  on  the 
statistical  method.  While  it  penetrates  to  the  foundation 
of  this  peculiar  procedure,  tested  by  long  experience,  the 
logical  contents  of  the  method  must  on  the  one  side  de- 
velop into  a  system  the  theory  of  statistics,  and  upon  the 
other  it  must  appear  what  form  the  technique  of  statistics 
should  assume  in  order  to  satisfy  the  requirements  made 
by  the  statistical  method,  theoretically  and  critically  de- 
veloped. 

What  in  general  should  be  regarded  as  statistical  method, 
which  is  the  subject  of  our  investigation,  can  be  gathered 
from  its  relation  to  logic,  and  from  a  survey  of  its  specific 
leading  thoughts. 


io6  Annals  of  the  American  Academy. 

§61.  relation  of  the  statistical  method  to  logic. 

From  the  history  of  statistics,  the  method  appears  to 
us  empirically  as  a  procedure  of  obtaining  judgments  and 
conclusions  as  to  the  relations  of  a  mass  of  changeable 
and  variable  things,  by  an  enumeration  of  characteristic 
qualities. 

More  briefly  the  same  thought  may  be  expressed  as 
the  method  of  judging  collective  phenomena  from  the 
results  of  enumerations. 

Scientific  logic  might,  as  §§  57  and  58  show,  express  the 
i  contents  of  this  sentence  more  precisely,  thus  :  the  statisti- 
**  ical  method  is  a  process,  based  on  an  enumeration  of  char- 
acteristic phenomena,  of  forming  empirical  judgments  and 
I  conclusions  relating  to  the  varied  and  complicated  aggre- 
gates of  existence.  It  is  used  where  the  experimental 
investigation  of  an  individual  or  collective  object  is  pos- 
sible neither  by  induction,  the  conclusion  from  the  special 
to  the  general,  or  by  deduction,  the  conclusion  from  the 
general  to  the  special. 

The  meaning  of  the  definition  must  be  explained.  All 
actual  existence  appears  to  man  as  inexhaustible  multipli- 
city. It  appears  to  his  thinking  powers  as  made  up  of 
certain  things  with  constant  qualities  despite  the  changing 
appearances.  From  the  constancy  of  these  qualities  we 
form  ideas. 

Of  the  things  thus  divided  by  ideas  we  know  actually 
but  few  exactly,  by  closer  view,  or  strict  experiment;  to 
the  rest,  on  finding  single  qualities,  we  apply,  inductively 
or  deductively,  the  presumption  of  similar  qualities,  and, 
as  experience  shows,  the  nature  of  things  permits  this  in  a 
degree  sufficient  for  ordinary  purposes. 

No  one  thing  is  however  actually  identical  with  another, 
no  one  can  occupy  the  space  of  another,  and  all  things 
which  follow  each  other  in  time  are  different.  Each  is  an 
individual,  and  has,  as  such,  certain  qualities  which  dis- 


Theory  and  Technique  of  Statistics.  107 

tinguish  it  from  every  other.  All  things  can  be  considered, 
according  to  the  point  of  view,  as  single,  or  as  in  com- 
bination, forming  larger  things.  Here  we  derive  the  ideas 
of  individuals  and  collectives  or  aggregates.  Each  one  of 
them  can  be  dissolved  finally  into  a  multiplicity  of  things 
simply  inexhaustible  for  human  observation,  and  as  diffi- 
cult of  complete  comprehension  in  its  constitution  as  in  its 
variations.  Each  thing  forms,  therefore,  according  to  the 
conception  of  the  moment,  a  unit  or  an  aggregate.  Con- 
sidered as  an  aggregate,  it  is  divisible  even  to  the  atoms, 
into  the  most  various  constituent  objects.  The  investi- 
gation of  all  these  parts,  which  appear,  according  to  the 
point  of  view,  as  individuals  or  collectives,  exceeds  the 
power  and  resources  of  any  observer.  According  to  its 
nature,  such  an  accumulation  of  dissimilar  objects  permits 
no  satisfactory  knowledge  of  its  full  content,  of  the  inner 
relations,  and  of  the  possible  expectation  of  permanency 
or  change,  by  induction  or  deduction,  which  could  only 
deal  with  the  single  objects.  Much  less  is  the  possibility 
conceivable  of  acquiring  by  experiment  any  knowledge  of 
the  continually  changing  multiplicity  in  each  single  thing, 
and  in  mutual  relations  and  conditions  of  them  all. 

The  method  of  statistics,  immaterial  whether  it  be  con- 
sidered as  a  general  one  of  alljsmpirical  ^cien^ce,  or  as 
specifically  statistical  in  every  case  of  its  application, 
appears  therefore  as  the  means  of  obtaining  knowledge 
as  to  aggregates,  i.  e.y  things  conceived  in  the  confused 
and  variable  multiplicity  of  their  components. 

§  62.   THE   LEADING  THOUGHTS  OF  THE  STATISTICAL  METHOD. 

The  method  of  statistics  must  unconditionally  abandon 
the  effort  to  investigate  completely  the  inexhaustible  dif- 
ferent combinations  of  the  aggregates.  But  its  fundamental 
idea  is  to  penetrate  in  a  limited,  yet  systematic  way,  into 
the  aggregate  in  order  to  ascertain  whether  and  how  often 
certain  things  are  to  be  found  there,  or  how  often  they 


y 


108  Annals  of  the  American  Academy. 

pass  in  and  out  of  it.  This  search  and  enumeration  is  the 
simplest  observation  possible,  not  influencing  in  any  way 
the  condition  of  the  aggregate.  The  result  can,  in  the  first 
instance,  be  only  a  more  or  less  defective  description.  The 
statistical  method  aspires,  however,  to  draw  conclusions 
from  such  enumerations,  as  to  the  relative  measure  of  the 
phenomena,  the  causal  connection,  and  the  expectation  of 
regular  reappearance  of  the  things  counted. 

The  idea  is,  thus,  to  approach  the  investigation  of  the 
multiplicity,  with  a  certain  purpose  in  view,  and  to  observe 
merely  such  things  whose  number  in  the  particular  aggre- 
gate it  is  necessary  to  ascertain  for  this  purpose. 

Things  which  are  to  be  sought  must  be  known  before- 
hand. When  it  is  purposed  to  find  their  number  the  idea 
chosen  in  advance  must  designate  something  capable  of 
enumeration  which  can  serve  as  the  unit  of  the  count. 
This  presupposes  that  it  can  be  distinguished  in  the  con- 
fused and  changing  real  multiplicity  of  the  aggregate  as  a 
certain  object,  with  definite  perceptible  qualities. 

All  objects  whose  characteristics  correspond  with  those 
of  the  unit  selected  are  to  be  counted.  With  the  sum 
which  results  from  this  counting  the  first  step  demanded 
by  the  statistical  method,  the  methodical  enumeration,  has 
been  taken.  As  far  as  the  purpose  of  the  problem  requires 
the  enumeration  of  a  group  of  different  things  instead  of 
that  of  a  definite  thing,  it  must  take  place  in  the  same 
way  for  each  distinct  thing. 

The  description,  by  means  of  the  number  of  any  kind 
of  things,  can  form  the  basis  of  a  methodical  judgment 
only  when  the  number  can  be  measured.  The  meaning  is 
not  at  once  apparent,  but  depends  upon  the  relation  to  a 
certain  scale.  This  scale  can  only  be  derived  by  seeing 
low  large  or  small  is  the  number  of  units  in  the  aggregate 
investigated  in  comparison  with  the  average  number  of 
the  same  units  found  in  analogous  aggregates.  Such  ag- 
gregates are  analogous  which,  considered  either  as  indi- 
viduals or  collectives,  come  in  the  same  category.     The 


Theory  and  Technique  of  Statistics.  109 

comparison  may  be  as  different,  according  to  the  special 
purpose,  as  the  conception  of  the  aggregate  as  a  unit. 
Upon  this  quantitative  relation  further  judgments  may  be 
based. 

Certain  points  for  the  determination  of  causal  connec-  k 
tions  can  be  obtained,  if  the  selection  of  the  things 
counted  had  this  end  in  view,  or  suffices  for  the  purpose. 
The  greater  measure  of  cause  must  bring  about  the  greater 
measure  of  effect.  In  the  aggregate  investigated  only 
that  measure  of  things  can  be  recognized  as  an  essential 
or  prominent  cause  which,  by  comparison  with  analogous 
aggregates,  appears  to  be  in  a  functional  relation  to  the 
effect.  When  units  which  express  the  effect  or  cause  directly 
are  not  suited  to  enumeration,  others  must  be  selected 
which  furnish  an  indirect  or  symptomatic  evidence.  If  no  «- 
functional  relation  exists  between  the  units  which  have 
been  chosen  each  time  with  reference  to  probable  causal 
relations,  we  have  simply  discovered  that  of  the  possible 
causes  considered  all  are  inapplicable. 

From  the  judgment  as  to  causality  the  last  step  leads  toL; 
that  of  probability.  The  same  causes  bring  about  the  same 
effects  under  the  same  conditions.  Under  like  circum- 
stances the  average  measure  of  things  in  analogous  aggre- 
gates would  also  be  the  most  probable  in  that  to  be  inves- 
tigated. The  average  relation  of  cause  and  effect  which 
appears  among  them  could  also  be  considered  as  the  regu- 
lar one.  When  regularities  are  observed  they  are  to  be 
considered  as  based  upon  like  circumstances.  .With  this 
judgment  as  to  the  expectation  of  phenomena  the  last  aim 
of  the  problem  of  penetrating  into  the  multiplicity  of  the 
aggregate  is  attained. 

On  account  of  the  necessity  of  observing  and  counting 
considerable  numbers  of  distinct  units  in  a  series  of  anal- 
ogous aggregates  this  process  requires  generally  very  con- 
siderable expenditure  of  effort.  Nevertheless,  it  leads  only 
to  a  partial  description,  and  at  the  most  to  an  approximate, 
an  hypothetical  judgment  as  to  the  inner  structure  of  the 


no  Annals  of  the  American  Academy. 

investigated  aggregate.  But  the  impossibility  of  investi- 
gating each  single  thing  with  experimental  precision  is 
common  to  all  empirical  sciences.  Inductive  and  deduc- 
tive judgments  are  also  hypothetical.  The  results  of  the 
^statistical  researches  do  not  refer  so  much  to  the  typical 
phenomena,  which  are  the  premises  for  inductive  and 
deductive  reasoning,  but  consist  rather  in  a  classification 
of  the  non-typical,  which  is  unattainable  in  any  other 
manner. 

Formally,  the  procedure  consists  of  two  stages,  one  pre- 
paratory, which  counts  the  units  in  the  aggregate  selected 
for  the  specific  purpose,  and  describes  the  same  by  means 
of  totals;  the  other,  or  completing  stage,  which,  obtaining 
for  comparison  the  sums  from  enumerations  of  similar 
units  in  different  analogous  aggregates,  forms  judgments 
on  the  relations  of  quantity,  of  the  causality  and  the  prob- 
ability or  regularity  of  the  phenomena.  The  technique  of 
the  method  follows  closely  these  logical  steps. 

The  theory  of  statistics  has  for  its  object  to  establish 
the  proper  foundation  for  each  stage  of  the  process,  and 
thus  determine  the  principles  according  to  which  in  a 
given  case  we  may  test  the  accuracy  of  statistical  results 
and  the  mode  of  obtaining  them. 


A.   THE   PRINCIPLES   OF   ENUMERATION. 
I.  Fundamental  Conceptions. 

§  63.    EMPIRICAL  CONDITIONS    OF  THE   ENUMERATION. 

The  first  step  of  the  statistical  method  indicated  by  the 
general  outline  of  the  procedure  is  that  of  the  enumeration. 
Characteristic  things  in  the  multiplicity  to  be  investigated 
are  to  be  ascertained  with  respect  to  their  number  as  they 
exist  in  it,  or  as  they  enter  and  leave  it. 


Theory  and  Technique  of  Statistics.  hi 

To  define  in  sharp  and  concise  terms  the  conditions  of 
this  first  step  as  well  as  of  the  further  processes  is  not 
without  difficulty.  In  particular  it  may  be  observed  that 
in  regard  to  necessary  requirements  of  the  method  com- 
plicated problems  are  often  more  comprehensible  than  the 
most  simple  ones. 

It  might  readily  appear  that  the  enumeration  of  any- 
thing, whether  for  statistical  purposes  or  for  the  purposes 
of  daily  life,  a  mere  counting-off  according  to  the  numeri- 
cal series,  was  a  complete  operation,  whose  aim  was 
attained  absolutely  without  any  reference  to  the  consid- 
erations mentioned  in  the  preceding  paragraph.  That  this 
view  is  erroneous  appears  readily  by  carefully  observing 
any  empirical  attempt  to  count. 

Suppose  someone  were  asked  to  count  paper  or  fruit 
lying  before  him.  He  would  see  at  once  that  before  begin- 
ning he  must  settle  which  of  the  objects  should  be  con- 
sidered as  fruit  or  paper,  for  the  purpose  in  view.  The 
explanation  given  must  be  perfectly  clear  and  perceptible 
to  the  person  counting.  Further,  it  must  be  settled  what 
is  a  piece  of  paper,  or  fruit,  and  whether,  perhaps,  fruit  is 
to  be  counted  by  piece  or  weight,  or  the  paper  by  the  size 
of  the  sheets.  A  change  in  these  particulars  could  not 
take  place  during  the  count.  Besides,  it  must  be  clearly 
defined  what  the  words  "  before  him "  express  ;  that  is, 
there  must  be  evidently  a  limit  of  space.  There  must  be  . 
a  limit  of  time  during  which  pieces  should  not  be  removed 
nor  added.  If  objects  change  their  positions  during  the 
count,  they  must  be  considered  as  changing  objects,  and 
measures  must  be  framed  for  their  treatment.  Simple  as 
these  conditions  may  appear,  no  one  can  remain  unfulfilled 
if  the  result  of  the  enumeration  is  to  be  correct  or  in 
accordance  with  the  intentions  of  the  questioner. 

They  need  not,  it  is  true,  always  be  expressed,  but 
the  most  complete  understanding  must  exist  between 
the  questioner  and  the  counter  as  to  the  smallest  de- 
tail.    It  is  not  to  be  doubted  that  these  requirements  are 


V 


H2  Annals  of  the  American  Academy. 

alike  indispensable  for  the  greatest  and  smallest  problems 
in  enumeration.  What,  however,  is  their  theoretical 
significance  ? 

§  64.  enumeration  and  calculation. 

The  complex  conditions  of  the  empirical  process  of 
counting  indicate  that  these  peculiarities  have  a  basis  in 
the  fundamental  relations  of  logical  knowledge.  Enumera- 
tion presupposes  the  idea  of  number.  Number  is  one  of 
the  earliest  abstractions  that  arose  in  the  formation  of  ideas. 
As  soon  as  thought  grasps  objects  and  distinguishes  be- 
tween them  in  classification,  it  is  impossible  to  escape  the 
notion  of  plurality.  Things  agreeing  in  their  conceptions 
appear  no  longer  as  isolated  things,  but  as  several  of  the 
same  species.  The  necessity  of  dealing  in  thought  with 
indefinite  pluralities,  and  of  expressing  them  in  communi- 
cation to  others,  makes  itself  felt  very  early  in  the  forma- 
tion of  language.  There  is  hardly  a  language,  however 
crude,  which  lacks  the  plural  denominations.  But  the 
plural,  and  evidently  also  the  dual,  are  not  numerical 
expressions.  The  dual  seems  to  be  the  expression  for  the 
frequent  symmetrical  double  phenomena  of  nature,  as  the 
eyes,  hands,  etc.  (W.  v.  Humboldt,  Ueber  den  Dualismus, 
1828.) 

Number  is  developed  first  in  the  progress  of  conscious 
observation  from  one  thing  to  another  similar  one.  It 
presupposes  that  the  idea  of  the  thing  is  conceived  of  as 
a  unit.  Number  is  not  formed  by  observing  1  and  1  and 
and  1,  or  placing  them  in  succession.  It  is  formed  when 
in  a  continuous  observation  each  occurrence  of  the  unit  is 
grouped  with  those  which  have  already  taken  place,  and 
an  expression  given  to  each  successive  group.  Each 
expression  indicates  the  total  of  all  occurrences  of  the  unit 
up  to  a  given  point  of  time.  Numerical  terms  belong  to 
the  oldest  traditions  in  all  languages,  and  yet  the  difficulty 
of  counting  and  retaining  numerical  ideas  is  shown  by  the 


Theory  and  Technique  of  Statistics.  113 

fact  that  many  races  have  no  numerals  beyond  three  or 
five. 

The  expressions  corresponding  to  the  successive  groups  «/ 
of  units  form  the  numerical  series.  In  counting  concrete 
things  memory  applies  the  numerical  order  to  the  obser- 
vations of  experience  to  determine  how  often  the  thing 
which  forms  the  unit  has  been  found.  This  finding  things 
by  observation  is  a  real  operation,  and  where  the  enumera- 
tion takes  place  in  the  recollection,  it  is  an  image  of  the 
real  world. 

The  succession  of  expressions  in  the  numerical  series  is 
a  succession  of  totals.  The  numerical  series  can  be  com- 
pletely separated  from  concrete  things  and  be  continued 
without  aid  from  them.  It  forms  in  that  case  a  succession 
of  ideas,  each  of  which  exceeds  the  sum  preceding  by  one 
unit.  This  order  permits  a  progress  by  sums  more  than 
unity,  as  well  as  a  division  into  series  of  pluralities.  This 
facilitates  the  use  of  numerical  signs,  mere  figurative  images 
of  the  numerical  expressions. 

The  consideration  of  the  abstract  numbers  and  the  re- 
lations of  numerical  series  awakened  much  interest  at  an 
early  date,  and  led  to  deductive  conclusions  from  the  ideas 
of  the  totals.     Thus  were  founded  calculation  and  mathe-  ' 
matics,  which  appear  to  be  the  oldest  human  sciences. 

It  would,  however,  be  a  mistake  to  see  in  the  early  and 
astounding  development  of  mathematical  calculation  also 
a  development  of  enumeration.  On  the  contrary,  this  art 
remained  all  the  more  neglected.  Closer  consideration 
shows  that  calculation  has  nothing  in  common  with  enu-V> 
meration  except  the  number.  It  can  proceed  apparently 
from  actual  existing  pluralities,  but  only  apparently,  for  it 
depends  entirely  upon  the  idea  of  the  identity  of  the  units. 
It  can  apply  this  idea  to  any  object,  but  in  reality  the  objects 
are  not  identical,  and  this  cannot  influence  the  idea  of  the 
units.  Calculation  necessarily  deprives  the  unit  with  which 
it  operates  of  every  specific  content,  and  perceives  in  each 
number  only  a  certain  quantity  of  wholly  empty  and  abstract 


H4  Annals  of  the  American  Academy. 

units,  which  permit  only  repetitions  and  divisions  just  as 
empty  and  abstract.  All  judgments  and  conclusions  of  , 
calculation  are  therefore  analytical.  Every  logical  thinker 
obtains  by  correct  conclusions  from  the  first  premises  the 
final  results  of  all  arithmetic  without  actual  experience. 
Upon  this  analysis  is  founded  the  science  of  mathematics. 
With  empty  numerical  conceptions  it  can  combine  only 
similar  ideas  of  corporeal  dimensions,  point,  line,  surface, 
and  volume.  All  these  ideas  are  so  empty  and  abstract, 
that  they  can  be  represented  by  no  phenomena  of  actual 
existence,  nor  do  they  correspond  to  any.  All  construc- 
tions are  entirely  ideal.  None  of  their  propositions  con- 
tains a  synthesis.  All  these  propositions  and  formulas 
simply  relieve  the  investigator  by  the  aid  of  memory  from 
undertaking  the  almost  insurmountable  labor  of  repeating 
in  his  own  thought  the  abstractions  of  centuries. 

Here  we  see  the  difference  between  enumeration  and  y 
calculation.  Calculation  elaborates  by  analysis  the  neces- 
sary consequences  from  given  ideas  of  magnitude,  with- 
out asking  whether  or  not  these  ideas  correspond  to 
any  reality.  Enumeration  endeavors  to  ascertain  how 
often  a  designated  unit  is  present  in  a  limited  reality  and 
is  a  thoroughly  real  and  synthetic  operation.  As  reality 
is  concrete,  so  must  the  unit  be  also,  and  must  be  found 
by  concrete  methods.  From  calculation,  which  can  never 
undertake  a  large  or  small  task  in  practical  enumeration, 
the  latter  can  obtain  assistance  only  when  the  actual  unit 
is  found  in  typical  division  or  multiples,  so  that  the  divisors 
a|nd  multiples  can  be  calculated  from  the  sums  counted; 
i.  e.}  can  be  ..derived  by  analysis. 

§65.    ENUMERATION    OF   THINGS    AND     MEASUREMENT   OF 
QUALITIES. 

I  The  distinctive  theoretical  peculiarities  of  enumeration 
J  require  that  the  collective  phenomena  which  statistics  are 
f  to  investigate  must  have  the  character  of  real  independent 


\ 


Theory  and  Technique  of  Statistics.  115 

things  in  order  to  be  counted.  They  may  indeed  exist 
merely  in  thought  or  be  counted  in  memory,  having  their 
limits  fixed  in  our  imagination,  but  in  one  way  or  the 
other  they  must  be  fixed  and  accessible  to  observation. 
This  requirement  is  perfectly  comprehensible  for  well- 
rounded  concrete  objects,  as  men,  houses,  ships.  It  be- 
comes a  question,  however,  how  the  numerous  distinctions 
are  to  be  treated,  which  result  from  the  qualities  of  such 
objects,  and  again  how  a  phenomena  may  be  utilized  for 
the.  investigation  when  it  does  not  appear  to  be  so  de- 
finitely limited. 

A  necessary  premise  of  enumeration  is  that  all  the  qual- 
ities of  an  object  which  characterize  it  as  the  unit  of  the  < 
count  must  be  fixed  and  invariable  for  the  period  of  the  I 
observation  upon  which  the  count  is  to  be  based.     As  the 
statistical  observation  is  always  instantaneous,  or  at  least 
must  be  regarded  so,  and  as  the  quality  always  attaches  to   ( 
an  object  and  never  exists  without  it,  the  quality  cannot 
be  variable  for  the  statistical  observation ;    for  when  the 
quality  changes  so  does  the  object  also.     The  change  in 
the  quality  would  necessitate  two  enumerations.     In  the 
two  the  object  is  different,  as  explained. 

Qualities  are  never  counted,  but  simply  the  objects  pos-/({ 
sessing   one   quality   or   another.     On   the   contrary,  air  // 

qualities  of  things  can  be  measured,  and  this  is  always/  / 
necessary  if  it  is  desired  to  observe  the  exact  differences 
in  the  same  quality. 

Every  quality  of  a  thing  is  perceptible  to  us  through 
impressions  of  the  senses,  and  upon  the  greater  or  less 
force  of  these  impressions  depends  their  measure,  or  their 
proportion.  To  observe  the  difference  in  which  a  quality 
appears,  we  seek  certain  easily- found  limiting  points,  and 
divide  the  space  between  them  into  equal  parts  to  form  a 
scale.  One  division  forms  the  unit  of  measure,  which  in 
an  observation  will  be  found  either  in  multiples  or  frac- 
tions. 

The  qualities  of  things  which  are  most  frequently  the 


116  Annals  of  the  American  Academy. 

subject  of  measurement,  are  magnitude  (measures  of  length, 
surface,  volume),  gravity  (measures  of  weight),  duration 
(measures  of  time),  value  (money,  the  measures  of  cur- 
rency). Measures  can  also  be  obtained  for  the  intensity 
of  other  qualities.  For  color,  heat,  sound,  hardness,  such 
measures  are  quite  familiar. 

Every  regular  progressive  gradation  contains  the  ele- 
ments of  a  measure  in  the  succession  of  its  parts.  But  it 
can  be  utilized  only  when  an  invariable  known  scale  is 
taken  as  a  basis.  The  ordinances  of  weights  and  measures 
of  the  governments  rest  upon  such  bases.  They  should 
always  be  founded  upon  a  normal  measure,  certified,  as  far 
as  possible,  by  physics. 

As  in  every  measurement  the  number  of  the  units  of 
measure  must  be  ascertained,  it  is  evident  that,  strictly 
speaking,  no  measurement  can  be  obtained  without  enu- 
meration. Yet,  counting  off  the  degrees  of  a  quality  is 
different  in  its  nature  from  the  statististical  enumeration. 
Statistics  use  it  only  exceptionally,  partly  as  a  supplement 
to  the  observations,  partly  as  a  means  of  making  them 
objective. 

The  first  case  occurs  when  things  of  the  same  general 
class  are  to  be  distinguished  in  the  enumeration  according 
M  n  to  certain  degrees  of  a  quality — e.  g.t  horses  according  to 
ages,  houses  according  to  the  number  of  stories.  The 
enumeration  of  the  degree  of  quality  is  only  preparatory 
to  the  enumeration  of  the  things  differentiated.  If  persons 
are  to  be  numbered  in  the  census  according  to  ages,  this 
preparation  of  the  classes,  etc.,  like  many  other  measure- 
ments not  to  be  carried  out  at  the  instant,  cannot  be  under- 
taken by  the  enumerating  official.  Distinctions  easily 
recognized  or  estimated,  can  naturally  be  made  in  con- 
nection with  his  observations. 

The  other  case  occurs  when  the  things  have  in  them- 
selves no  sufficient  limitation  as  independent  objects,  such 
as  air,  rain,  area,  arable  land — time  and  space  generally; 
or,  indeed,  actual  things,  such  as  products,  grain,  iron, 


h 


Theory  and  Technique  of  Statistics.  117 

wood,  where  the  number  of  pieces  furnishes  no  practical 
nor  sufficiently  distinct  idea.  In  this  case  the  quality, 
measure,  or  weight  must  replace  the  limitation  lacking  in 
the  thing  itself.  But  the  enumeration  cannot,  nevertheless, 
be  performed  according  to  the  quality,  but  only  according 
to  the  units  of  quality,  thus  established  in  the  thing  to  be 
counted. 

The  quality  alone  can  never  replace  the  thing.     One 
cannot  count  ages  without  the  persons,  or  weights  without 
the  goods  to  which  they  belonged ;  and  it  is  impossible  to 
count  prices,  market  prices,  and  similar  data  of  measure 
or  value  without  the  articles  for  which  they  are  counted  or 
calculated.  Every  such  general  datum  requires,  if  it  is  to  be 
correct  and  not  merely  an  inexact  estimate,  classification  of 
the  objects  according  to  the  prices  paid,  noting  the  num- 
ber or  the  weight  of  the  things  of  each  class,  and  calcula- 
tion of  the  price,  as  the  average  of  the  number  of  units 
reduced  to  a  uniform  measure.     The  fundamental  premise \       *g 
of  statistical  enumeration,  whether  measurements  of  quality  \  lV 
come  in  question  or  not,  is,  first  of  all,  the  real  objective  / 
nature  of  the  unit  of  enumeration. 

§66.    THE   UNIT   OF   ENUMERATION. 

Intimately  connected  with  the  requirement  of  the  method 
that  only  concrete  things  can  be  objects  of  the  enumeration, 
is  the  further  one  that  these  objects  can  only  be  enumerated 
according  to  a  previously  well-defined  idea.  The  things 
to  be  included  in  the  enumeration  must  correspond  entirely 
with  the  preconceived  notion  of  the  unit  of  enumeration. 
Nothing  contained  in  the  aggregate  which  corresponds  to 
this  idea  can  be  passed  by  unnoticed.  This  is  the  indispens- 
able condition  of  the  correct  enumeration,  and,  therefore, 
of  paramount  importance  as  the  basis  of  the  entire  process.. 

All  essential  characteristics  of  the  unit  of  enumeration 
must  be  definitely  fixed  before  the  process  begins.  They 
cannot  be  changed  by  any  modification  or  seeming  expla- 


II 


u8  Annals  of  the  American  Academy. 

nation  during  the  process.  The  unit  should  be  so  defined 
as  to  leave  no  room  for  doubt.  This  is  essential  to  the 
uniformity  of  the  enumeration,  and  indispensable  for  the 
subsequent  use  of  the  results.  But  it  is  seldom  possible 
to  determine  expressly  for  the  enumerator  the  whole  group 
of  characteristics  essential  to  the  idea  of  the  unit  of  enu- 
meration. The  common  usage  of  the  language  must,  with 
the  greatest  possible  simplification,  serve  as  the  basis  of 
the  idea.  Often  it  is  sufficient  in  itself,  as  "  man,"  "animal," 
"tree."  Certain  ideas  have  a  legal  meaning  or  one  equally 
capable  of  proof,  such  as  "letter,"  "merchant,"  "criminal." 
But  it  must  always  be  considered  whether  the  word  in  com- 
mon usage  is  applicable  to  the  enumeration  of  independent 
things,  or  requires  some  more  precise  definition,  as  "house," 
"dress,"  "book." 

As  a  rule,  it  is  necessary,  besides  the  designation  of 
common  usage,  to  determine  expressly  certain  particular 
characteristic  qualities.  This  is  especially  true  where 
things  of  the  same  general  class  are  to  be  counted  differ- 
ently, according  to  certain  features.  Here  the  process  of 
measuring  qualities,  described  in  §65,  comes  into  play.  At 
the  same  time  it  may  be  observed  that  the  ideas  of  quality, 
which  seem  to  have  great,  even  mathematical,  exactness, 
do  not  apply  strictly  in  reality,  as,  for  instance,  the  term 
"  spherical."  Further,  it  must  be  remarked  that,  especially 
in  the  designation  of  qualities,  the  use  of  language  is 
exceedingly  variable,  and  can  seldom  dispense  with  an 
exact  scale. 

A  systematic  selection  of  essential  characteristics  facili- 
tates the  proper  comprehension  of  them.  The  value  of 
the  determination  of  the  idea  agreed  upon  depends  on  the 
capacity  of  the  observer.  For  a  group  of  a  few  experi- 
enced enumerators,  the  units  of  enumeration  can  be  de- 
fined very  differently  than  when  numerous  different  and 
inexperienced  persons  are  drawn  into  the  service. 


Theory  and  Technique  of  Statistics.  119 

§67.    THE   FIELD   OF   THE   ENUMERATION — THE    LIMITS   OF 
TIME   AND   SPACE. 

The  consideration  of  a  mere  off-hand  counting  of  things 
(§  63),  shows  that,  besides  a  definite  unit,  the  enumeration 
requires  a  limit  of  the  time  and  space  in  which  it  was  to 
be  made. 

The  objects  which  are  to  be  counted  may  form  either  a^ 
stationary  number,  i.  e.,  be  found  in  the  same  space  at  the 
same  moment;  or  a  succession  or  movement,  i.  e.t  pass 
through  the  same  space  in  a  certain  period  of  time,  or 
they  can  appear  variously  in  the  given  limits  of  time  and 
space.  If  the  same  object  be  found  more  than  once  in  the 
given  time,  it  becomes  necessary  to  determine  whether  it 
is  to  be  counted  but  once  or  oftener. 

For  all  these  cases,  it  is  to  be  remarked  that  while  the 
objects  to  be  enumerated  may  completely  fill  out  the  given 
limits  of  time  and  space,  this  is  only  accidental,  and,  ac- 
cording to  the  nature  of  the  enumeration,  rather  improbable. 
For  the  problem  is,  to  find  these  units  in  a  given  time  and 
space.  They  may  or  may  not  be  found.  The  needs  of 
the  enumeration  have  been  complied  with,  even  when  the 
result  is  zero. 

Thus  it  is  evident  that  the  limitation  of  time  and  space 
does  not  take  place  in  the  unit,  but  upon  some  connected 
fundament,  considered  as  a  whole,  which  is  the  field 
of  the  investigation.  Such  a  field,  limited  in  time  and 
space,  in  which  real  objects  are  to  be  enumerated,  must 
consist  necessarily  of  a  more  or  less  extended  portion  of 
actual  space,  either  at  a  given  instant  or  for  a  longer 
period.  Actual  space  is  not  a  vacuum,  but  filled  with  an 
immense  multiplicity  of  real  things,  and  in  the  course  of 
any  longer  or  shorter  period  these  can  change  in  incon- 
ceivably numerous  ways. 

Each  field  thus  limited  must  of  necessity  be  conceived 
as  a  whole,  as  individual  or  collective.  But  every  unit 
can,  as  we  have  seen,  be  considered  in  regard  to  its  inter- 


V' 


120  Annals  of  the  American  Academy. 

nal  complexity,  as  an  aggregate,  and  thus  become  the  field 
of  an  enumeration. 

Thus  it  appears  that  the  idea  of  the  aggregate,  the  in- 
vestigation of  which  by  enumeration  forms  the  purpose 
of  statistics,  is  included  in  the  idea  of  an  enumeration 
strictly  considered. 

II.  The  Process  of  Enumeration. 

§  68.   OBSERVATION  AND   SUMMATION. 

The  enumeration  investigates  how  often  the  unit  chosen 
is  to  be  found  in  the  given  aggregate.  It  consists,  there- 
fore, of  an  observation  of  the  units,  and  a  summation  of 
the  observed  cases  of  its  existence. 

The  observation  must  distinguish  the  components  of  the 
aggregate  into  such  things  as  possess  the  characteristics 
of  the  unit  and  such  as  do  not.  It  must  be  so  planned 
that  everything  which  might  possibly  correspond  to  the 
unit  shall  be  noticed  and  examined  with  reference  to  the 
decisive  characteristics.  No  unit  should  be  omitted  or 
counted  more  than  once.  When  there  are  several  ob- 
servers this  must  be  avoided  by  a  careful  division  of  the 
field  among  them. 

The  observation  is  direct,  when  the  observer  searches 
the  entire  aggregate  himself  for  them ;  indirect  when  he 
has  his  resort  to  records  and  registrations  and  announce- 
ments and  lists  of  various  kinds.  If  the  fact  of  record  is 
conditioned  on  the  same  qualities  which  make  the  thing 
a  unit  of  enumeration,  the  observation  is  properly  in  the 
hands  of  those  who  make  the  records. 

For  records  which  serve  statistical  purposes  exclusively, 
specific  schedules  are  in  use.  They  seek  to  obtain  the 
notes  of  the  single  observations,  systematically  arranged 
according  to  the  required  points,  with  as  little  writing  as 
possible,  yet  definite  in  form  and  convenient  for  summar- 
izing.    If  they  form  a  system  of  coordinates,  in  the  lines 


Theory  and  Technique  of  Statistics.  121 

of  which  the  distinctions  of  the  unit  of  enumeration  are  to 
be  arranged  according  to  like  ideas,  they  are  called  lists. 
If  they  are  limited  to  a  single  unit,  whose  characteristics 
are  so  reported  that  afterward  distinctions  can  be  made  in 
the  summation,  they  are  called  cards.  (Statistik  d.  Deutschen 
Reiches,  Bd.  I.,  pp.  77,  103.) 

The  summation  is  direct  when  the  totals  are  given  in  the 
course  of  observation ;  indirect,  when,  as  is  usual,  the  single 
observations  are  noted  and  afterward  added  together.  A 
tabular  scheme,  which  presents  the  summations  of  the  re- 
sults systematically  and  in  conformity  with  the  purpose  of 
a  statistical  problem,  is  called  a  combination  formula.  (Cf. 
pp.  99,  395  of  work  above  quoted.)  -^ 

§  69.   SUBSTITUTES  FOR    ENUMERATION,   CALCULATIONS,   ESTI- 
MATES,   AND  THE  ENQUETE. 

Enumeration  by  observation  and  summation  of  the 
units  is,  as  a  rule,  a  very  extensive,  tedious,  and  expensive 
operation,  as  most  statistical  inquiries  are  concerned  with 
the  affairs  of  peoples  and  nations.  In  every  case  the  en- 
deavor must  be  to  make  the  solution  as  simple  as  possi- 
ble. But  it  is  often  altogether  impossible  to  attain  the 
practical  end  in  view,  unless  it  can  be  done  with  small 
means,  or  in  a  limited  period  of  time. 

Hence  operations  have  been  devised  which  can  be  used 
in  a  measure  as  substitutes  for  enumeration.  Such  sub- 
stitutes are,  however,  always  imperfect.  They  are  based 
on  the  effort  to  use  results  already  known,  in  order  to 
dispense  with  the  necessity  of  new  investigations. 

The  simplest  is  the  so-called  "  estimate."  It  is,  when 
based  upon  a  cursory  observation,  simply  a  very  inexact 
enumeration ;  when  it  is  formed  without  an  observation  it 
necessarily  supposes  previous  observations  on  the  basis  of 
which  a  species  of  inexact  enumeration  is  carried  out  men- 
tally.    To  do  this,  however,  one  must  be  permitted  to 


« 


(1 


■\ 


122  Annals  of  the  American  Academy. 

suppose  a  certain  degree  of  constancy  of  the  units  and 
the  aggregates. 

Another  means  to  this  end  is  sought  in  calculation. 
Enumeration  seeks  to  determine  the  unknown  frequency 
of  the  unit  in  the  aggregate,  but  a  calculation  must  be 
based  upon  known  elements.  If  a  unit  of  enumeration  is 
a  distinct  function  of  another,  the  number  of  the  latter 
can  be  calculated  from  that  of  the  former ;  and  conversely, 
when  one  such  unit  has  been  obtained  by  an  enumera- 
tion, there  is  obviously  no  need  of  one  for  the  other.  But 
calculation  cannot  replace  enumeration,  for  calculation  is 
always  analytical,  never  synthetical. 

The  use  of  probabilities,  so  frequently  applied  in  place  of 
enumeration,  can  only  replace  it  up  to  a  certain  point.  This 
is  not  because  it  is  hypothetical.  On  the  contrary,  such  a 
hypothetical  conclusion  as  to  a  number  must,  where  it  is 
critically  permissible,  be  regarded  as  the  highest  aim  of 
statistical  inquiry.  It  is  based  on  the  most  difficult  com- 
bination of  the  results  of  the  various  enumerations. 

The  method  known  as  expert  estimate  or  enquete  is 
generally  a  combination  of  these  various  modes  of  ob- 
viating a  direct  enumeration.  In  the  stead  of  actual 
results  of  enumeration,  it  deals  with  the  data  furnished  by 
persons  whose  knowledge  and  capacity  for  judging  ex- 
isting observations,  estimates,  enumerations,  elements  of 
calculation  and  probability,  renders  them  worthy  of  con- 
fidence. 

The  enquete  is  usually  applied  as  a  simplification  and 
acceleration  of  statistical  inquiries.  It  is  for  many  things 
the  only  form  of  investigation  which  can  be  used.  It  can- 
not be  dispensed  with,  where  the  organization  of  competent 
enumerators  to  go  over  the  entire  aggregate  is  not  feasible ; 
or  where  merely  such  enumerators  can  be  obtained  whose 
self-interest,  opposition  to  the  matter,  or  false  notions  stand 
in  the  way  of  correct  enumeration. 

But  if  the  results  of  an  enquete  are  to  be  statistically 
useful,  they  must  be  capable  of  replacing  completely  the 


Theory  and  Technique  of  Statistics.  123 

results  of  actual  enumeration ;  they  must  retain  the  com- 
plete precision  of  the  idea  of  the  unit  of  enumeration ;  they 
must  comprehend  the  entire  aggregate;  and  they  must 
express  numerically  and  distinctly  the  totals  estimated  as 
if  they  had  been  counted,  or  at  least  must  make  it  possible 
to  calculate  them. 

Enquetes  which  are  carried  on  with  an  indefinite  idea  as  / 
to  the  aggregate  and  the  unit,  or  express  their  opinions  \ 
without  any  definite  gradations  in  number  and  measure, 
are  nothing  more  than  general  descriptions.  They  are  of 
no  use  for  the  investigation  of  aggregates,  and  can  be 
utilized  only  for  such  purposes  as  are  served  by  a  subjec- 
tive description,  without  an  exact  comparison  of  relations. 

Allied  to  the  enquete  is  the  so-called  "political  arith- 
metic," where  it  endeavors  to  give  information  of  certain 
definite  conditions.  The  statistician  here  appears  as  an 
expert.  But  political  arithmetic  concerns  itself,  on  the 
one  hand,  with  general  problems  in  the  most  varied  fields 
of  statistical  research,  and,  upon  the  other  hand,  with 
questions  of  methods  and  arithmetical  conclusions  from 
the  results.     Hence  the  term  is  a  broad  one. 


§70.    POSSIBILITY  OF  ERROR   IN   ENUMERATION. 

Enumeration  is  a  practical  process  upon  actual  founda- 
tions, and  must  therefore  struggle  with  mistakes  and  im- 
perfections. Errors  in  observation  or  in  summing  up  are 
always  to  be  apprehended.  The  easier  it  is  to  mistake  the 
characteristics  of  the  unit  of  enumeration,  or  the  limits  of 
time  and  space,  or  to  judge  them  falsely,  the  more  must 
omissions  and  duplications  be  expected.  The  more  figures 
are  written,  and  the  less  the  calculations  are  proved,  the 
greater  is  the  probability  of  errors  in  transcribing. 

The  improvement  of  the  technique  must  seek  to  limit 
as  much  as  possible  the  sources  of  error,  but  they  are  no 
reproach  to  the  method  as  such.  Errors  in  the  observation 
may  be  subsequently  corrected,  when  the  existence  or  non- 


124  Annals  of  the  American  Academy. 

existence  of  the  units  falsely  counted  can  be  ascertained  for 
the  time  of  the  original  enumeration.  A  certain  possibility 
of  error  must  always  remain,  and  the  attempt  must  be 
made  to  estimate  its  extent. 

For  certain  purposes  the  presumption  of  even  small 
errors  can  render  the  result  useless,  whereas  in  other  cases 
even  very  considerable  errors  may  be  of  no  consequence. 
The  latter  is  particularly  the  case  when  the  problem  is 
sufficiently  solved  by  a  certain  maximum  or  minimum 
number  of  units.  The  more  restricted  the  purpose  the 
greater  may  be  the  possibility  of  error,  generally  speak- 
ing, but  the  more  general  the  purpose,  the  more  the  results 
must  serve  for  indefinite,  not  yet  known  problems,  the 
more  must  the  limits  of  possibility  of  error  be  contracted. 
An  unlimited  possibility  of  error  would  render  the  result 
worthless  for  all  purposes.  A  judgment  with  reference  to 
this  matter  is  indispensable  to  anyone  proposing  to  use  the 
numerical  results  obtained. 

Properly  prepared  statistical  enumerations  must  there- 
fore include  in  their  presentation  sufficient  explanation  of 
their  basis  and  processes  to  permit  a  conclusion  as  to  the 
possibility  of  error,  and  in  general  to  furnish  the  guaranty, 
that  for  the  usual  sphere  of  statistical  problems,  the  relia- 
bility of  the  figures  is  sufficient. 

§71.    PECULIARITIES   OF   THE   RETURNS. 

The  number  of  units  present  in  the  aggregate  can  be 
obtained  directly  by  observation  and  summation,  or  by 
complicated  calculations.  In  every  case  it  represents  a 
total — that  is,  a  definite  number  which  tells  how  many 
times  the  unit  has  been  found  in  the  mass. 

This  total,  because  a  total,  gives  no  picture  of  the  ar- 
rangement of  the  units  in  the  aggregate.  It  would  be  an 
egregious  error  to  suppose  that  anything  was  known  as 
to  the  position  of  the  units,  as,  for  instance,  a  map  shows 
the  positions  of  the  cities  of  a  country.     This  is  by  no 


Theory  and  Technique  of  Statistics 


means  the  case.  Every  single  unit  is  observed  at  the 
time  of  the  enumeration,  but  it  is  not  located.  It  disap- 
pears completely  in  the  final  result,  which  is  the  total  sum 
of  the  enumerated  units.  The  results  of  the  observation 
are  not  susceptible,  after  the  enumeration  is  complete,  of 
any  further  subdivision  of  either  time  or  space. 

If  it  is  possible  to  say,  as  is  often  done,  how  many  of  the 
enumerated  units  were  found  in  this  or  that  portion  of  the 
space  or  time  in  question,  it  must  be  clear  that  separate 
enumerations  have  been  made  for  these  portions.  The 
same  unit  of  enumeration  has  been  employed,  but  it  has 
been  applied  to  an  aggregate  corresponding  to  these  por- 
tions, and  necessarily  limited  in  time  and  space  in  the  same 
manner.  The  aggregate  to  be  investigated  has  been  sep- 
arated into  independent  minor  aggregates.  The  results  of 
these  enumerations  for  the  smaller  aggregates  may  be' 
combined  to  form  the  total  for  the  general  aggregate. 
But  in  so  far  as  the  enumeration  has  been  divided  into 
particular  enumerations  for  particular  aggregates,  the  re- 
sult for  each  aggregate  is  a  single  total,  incapable  of 
further  subdivision. 

Again,  the  results  furnish  information  only  as  to  the 
constitution  of  the  aggregate  and  not  of  the  units  of  enu- 
meration ;  for  the  unit  is  known  and  its  limits  prescribed 
before  the  enumeration.  To  fill  the  conditions  of  problems 
the  things  counted  must  correspond  to  this  idea.  They 
agree  because  they  fall  within  the  limits  of  this  character- 
istic idea,  but  only  so  far  as  this  is  the  case.  As  to  other 
peculiarities  their  constitution  may  be  very  different. 
Everything  counted  as  a  unit  must  necessarily  have  other 
characteristics  besides  those  in  question.  These  other 
characteristics  remain  unknown  quantities. 

The  addition  made  to  our  knowledge  is  simply  that 
things  which  correspond  to  the  given  idea  are  found  in  a 
certain  total,  or  possibly  not  at  all  in  the  aggregate.  As 
to  this  aggregate,  the  field  of  the  investigation,  there  is 
some  new  knowledge.     But  as  to  the  things  enumerated 


126  Annals  of  the  American  Academy. 

there  is  a  new  insight,  only  in  so  far  as  they  may  be  char- 
acterized by  their  presence  in  definite  numerical  relations 
in  the  aggregates  investigated. 

§  72.    ENUMERATION   OF  UNITS   IN   COMBINATION. 

The  problem  of  investigating  the  manifold  character- 
istics of  an  aggregate  from  the  number  of  fixed  known 
and  definite  things  which  go  to  make  it  up,  is  rendered 
easier  and  more  profitable  the  greater  the  number  of  things 
which  may  be  counted  and  the  more  they  may  be  brought 
into  combination.  This  combination  of  the  units  of  enu- 
meration may  be  of  several  kinds. 

The  different  units  may  be  related  simply  in  their  juxta- 
position. The  enumeration  finds  the  unit  A  (persons)  x 
times,  the  unit  B  (houses)  y  times,  and  the  unit  C  (horses) 
z  times.  The  judgment  is  that  x  A,  y  B,  and  z  C  are 
in  the  aggregate. 

The  units  can  be  chosen  from  their  relations  to  certain 
qualifying  ideas.  The  unit  A  can  be  counted  as  qualified 
by  several  characteristics ;  a  (male)  b  (single).  Then  the 
result  is  that  y  (A  +  a),  z  (A  +  b)  are  found  among  x  units 
of  A.  These  qualifications  may  or  may  not  exhaust  the 
idea  A.  They  may  describe  it  from  the  different  points  of 
view :  D  (arable  land)  enumeration  according  to  c  (area), 
or  d  (value),  hence  w  (D  +  c)  =  v  (D  +  d). 

The  choice  of  units  may  be  made  according  to  some 
supposed  causal  connection ;  e.  g.y  E  (children),  F  (teach- 
ers). The  result  is,  for  u  E  there  were  t  F.  Whether 
cause  and  effect  are  here  at  work,  and  if  so,  how,  is  not 
determined. 

The  greater  the  number  of  possible  relations  among 
the  units,  as  suggested  by  induction,  and  the  more  sys- 
tematically the  effort  is  made  to  bring  out  such  relations, 
so  much  the  more  must  the  numerical  data  obtained  add 
to  our  knowledge  of  the  conditions  existing  in  the  aggre- 
gate. 


Theory  and  Technique  of  Statistics.  127 

§  73.  results  of  the  enumeration. 

The  results  of  the  enumeration  form,  it  is  obvious,  a  de- 
scription of  the  subject  investigated.  This  description  is 
more  comprehensive  when  large  and  systematically  con- 
nected groups  of  different  units  are  counted.  It  is  attained, 
however,  when  the  enumeration  is  carried  through  with  a 
single  unit. 

It  must  be  recognized  that  such  a  description  would  be 
attained,  either  positively  or  negatively,  if  the  observer, 
having  before  him  a  real  field  of  view,  and  without  any 
knowledge  of  it,  should  conceive  a  certain  thing  as  a  unit, 
count  it  without  any  definite  purpose.  This  would  be  true 
whether  he  found  it  within  the  definite  limits  of  the  field 
or  not.  The  fact  that  it  is  a  conscious  problem  lends  a 
meaning  of  the  description  which  is  the  result  of  method- 
ical enumeration.  Essential  premises  are  drawn  from  this 
conscious  purpose,  which  cannot  be  separated  from  the 
process.  This  purpose  follows  necessarily  from  the  fact  > 
that  the  methods  of  statistics  are  applied  to  fill  out,  if  pos- 
sible, some  gap  which  inductive  and  deductive  methods 
have  consciously  left  open  in  the  investigation  of  the  mul- 
tiplicity of  actual  existences.  The  aggregate  investigated 
is  known  as  a  whole,  as  an  individual  or  collective  idea ; 
and  it  is  examined  in  its  composition  and  internal  connec- 
tions, which  are  unknown. 

This  examination  is  not  without  plan.  It  is  not 
directed  toward  any  chance  object,  but  the  enumeration 
bears  upon  a  unit  chosen  expressly  with  reference  to  its 
significance  for  our  knowledge  of  the  whole. 

So  simple  and  apparently  superficial  a  process  as  the 
mere  counting  of  certain  things  is  only  chosen  because  it 
is  believed  that  some  gain  in  knowledge  will  result  from 
the  determination  of  the  number. 

I  Statistics  presupposes  for  its  method  a  wealth  of  expe- 
riences and  abstractions.  The  methodical  description  ob- 
tained by  enumeration  rests  upon  a  basis  of  well-connected 


128  Annals  of  the  American  Academy. 

ideas,  which  is  to  be  further  built  up  by  the  results  attained, 
or  to  be  better  adapted  by  them  for  certain  definite  pur- 
poses. 

Nevertheless,  the  peculiar  barrenness  and  inflexibility  of 
this  summation  is  not  to  be  mistaken.  The  question  is  not 
of  this  mere  description,  but  of  the  real  importance  of  the 
gain  which  these  figures  promise. 

While  the  units  observed  correspond  to  real  facts,  these 
facts  are  determined  beforehand  by  fixing  certain  well- 
defined  characteristics,  not  by  exhausting  all.  The  only 
additional  determination  of  the  idea  of  the  phenomenon 
which  is  obtained,  is  whether  it  is  contained  once,  twice, 
more  frequently,  or  not  at  all,  in  the  aggregate.  Here  the 
size  of  this  number  is  of  decisive  value. 

Numbers  and  numerical  successions  have  a  certain 
gradation  in  themselves ;  i.  e.,  i  is  half  as  much  as  2,  and 
40  ten  times  as  much  as  4,  and  so  forth.  But  when  in  a 
certain  aggregate  A  is  found  10  times,  B  40  times,  and  C 
1000  times,  or  20  a  and  30  b  among  100  c,  these  figures 
give  obviously  no  measure  of  each  other,  nor  in  fact  any 
comprehensible  measure.  Whether  it  is  much  or  little  is 
impossible  to  tell. 

Empirically  it  may  indeed  appear  otherwise,  because  in 
our  general  thought,  and  by  recollection  of  numerous  sta- 
tistical enumerations,  we  have  a  number  of  hazy  ideas  as 
to  the  number  of  units  (men,  houses,  goods)  which  were  in  a 
certain  locality,  and  such  ideas  are  used  instinctively  as 
measures,  however  deficient  they  may  be. 

The  strict  methodical  process  cannot  rely  upon  such 
uncertain  support.  It  must  require  that  the  true  impor- 
tance of  figures  be  measured  on  an  exact  standard. 

Such  a  standard  might  be  obtained,  one  would  think,  by 
such  an  investigation  of  the  aggregate  as  would  show  how 
many  of  the  things  counted  it  ought  to  contain,  and  must 
contain,  conformably  to  its  essential  character,  and  in  what 
degree  it  had  the  capacity  or  possibility  of  containing  fewer 
or  less.     But  this  method  is  obviously  that  of  the  experi- 


Theory  and  Technique  of  Statistics.  129 

mental  investigation  of  the  aggregate  with  all  its  confused 
and  changing  complexities,  with  all  the  possible  combina- 
tions of  its  elements,  and  their  wealth  of  mutual  inter- 
relations. Such  an  investigation  may  be  said  to  be  im- 
practicable in  principle.  But  if  by  any  possibility  it  might 
appear  actually  possible,  it  could  not  be  avoided,  and  in 
that  case  the  statistical  method  would  be  rendered  super- 
fluous. 

Under  the  conditions  of  statistical  inquiry  it  is  not  pos- 
sible to  obtain  a  measure  of  the  results  of  the  enumeration 
of  an  aggregate,  simply  from  the  nature  of  the  aggregate 
as  apparent  from  the  enumeration.  With  the  demand  for 
such  a  measurement  the  whole  process  reaches  a  point 
where  it  can  no  longer  confine  itself  to  the  observation  of 
the  aggregate  to  be  investigated,  and  where  the  total  work 
of  enumeration,  however  complicated,  difficult,  and  exten- 
sive it  may  have  been,  is  clearly  recognized  as  only  of  a 
preparatory  character. 


B.  PRINCIPLES  OF  STATISTICAL  JUDGMENTS.      & 
I.  Quantitative  Relations. 

§  74.  THE  MEASURE  OF  QUANTITY  FROM  ANALOGOUS 
AGGREGATES. 

The  description  of  any  investigated  aggregate  by  a 
statement  of  totals  obtained  by  counting  its  component 
parts,  does  not  furnish  any  new  information,  unless  we  can 
form  a  judgment  of  the  meaning  of  these  sums.  Whether 
a  single  unit  or  a  number  of  units  has  been  counted,  is 
wholly  immaterial 

A  judgment  on  the  number  of  observed  phenomena 
must  necessarily  be  one  of  proportion ;  that  is,  of  a  quan- 
titative nature.  Are  the  figures  obtained  to  be  considered 
large  or  small,  and  if  so,  in  what  degree  ?     This  is  the 


y 


130  Annals  of  the  American  Academy. 

question  which  arises,  and  the  necessity  of  some  measure, 
some  scale  by  which  to  judge  the  results,  becomes 
obvious. 

Statistics  finds  this  measure  in  the  comparison  of  the 
results  obtained  for  similar  units  in  analogous  aggregates. 
These  may  be  the  fruit  of  previous  or  of  simultaneous 
investigations. 

The  proportion  which  the  different  units  of  enumeration 
bear  on  the  average  to  equal  portions  of  the  analogous 
aggregates  is  calculated,  and  the  limits  of  the  deviation  from 
the  average  in  both  an  ascending  and  a  descending  scale 
are  observed.  Thus,  a  measure  is  furnished  with  which  to 
judge  of  the  numerical  relations  of  the  units  in  any  par- 
ticular aggregate.  What  is  meant  by  analogous  aggre- 
gates scarcely  needs  explanation.  It  appears  clearly  that 
they  are  aggregates  which  considered  as  a  whole  come  in 
the  same  category. 

It  is  from  this  point  of  view  possible  to  conceive  of  the 
number  of  analogous  aggregates,  changing,  as  they  do, 
according  to  the  problem  in  hand,  as  almost  inexhaustible. 
The  number  may,  however,  be  very  small.  In  every  case 
it  is  limited  by  the  fact  that  we  can  actually  use  only  such 
aggregates  for  purposes  of  comparison  in  which  units 
similar  to  those  of  the  aggregate  investigated  are  or 
have  been  counted.  Hence  the  measure  of  comparison 
must  be  drawn  from  a  comparatively  restricted  group  of 
analogous  aggregates,  and  everyone  using  it  must  bear  in 
mind  upon  what  group  of  analogies  the  judgment  is  based. 

The  analogous  aggregates  are  sufficiently  known.  They 
are  not  chosen  from  those  manifold  and  confused  charac- 
teristics, which  are  the  subjects  of  statistical  inquiry,  but 
I  from  those  definite  qualities  which  as  a  whole  place 
them  in  some  general  class.  Conceived  as  a  whole,  they 
must  be  judged  by  inductive  methods,  and  it  can  be  seen 
which  have  more  importance  than  others  for  the  compari- 
son, and  which,  therefore,  would  constitute  more  valuable 
elements  of  the  scale.     This  building  up  on  information 


Theory  and  Technique  of  Statistics.  131 

gained  by  induction,  is  a  very  general  and  necessary  ele- 
ment of  statistics.  The  ideas  of  empirical  thought  are 
earlier  than  the  questions  of  statistics.  Inductive  knowl- 
edge is  only  supplemented  by  statistics  where  gaps  remain 
and  further  progress  is  barred. 

The  difficulty  of  the  process  does  not  lie  in  the  often 
very  limited  sphere  of-  analogies  which  can  be  used  in 
forming  the  scale,  but  rather  in  the  proper  conception  of 
the  aggregates  which  in  concrete  cases  may  be  looked 
upon  as  analogous. 

§  75.  THE  CHOICE  OF  ANALOGOUS  AGGREGATES. 

The  choice  of  analogous  aggregates  necessarily  depends 
upon  their  character  as  units.  This  depends  in  the  first 
place  on  that  particular  conception  of  the  aggregate  as 
an  entirety,  required  by  the  problem. 

In  this  connection  it  is  of  course  requisite  that  every  field 
of  statistical  investigation  may  be  generally  conceived  in 
its  entirety  as  a  single  thing,  whether  as  an  individual 
or  as  a  collective. 

Evidently,  statistical  enumeration  and  the  kind  of  de- 
scription which  follows  from  it  are  utterly  incapable  of 
characterizing  the  aggregate  as  individual  or  collective. 
All  essential  qualities  of  the  individual,  as  well  as  of  the 
collective,  which  are  conceived  as  fixed,  or  changeable, 
relate  to  its  organization  as  an  entirety.  But  the  statistical 
enumeration  concerns  only  certain  things  among  the  vari- 
ous elements  which  compose  this  entirety  and  determine 
their  number.  If  this  number  belongs  to  the  notion  of 
the  entirety,  then  it  is  typical.  But  in  that  case  it  would 
be  known  already  by  means  of  general  or  experimental 
observations,  and  have  found  a  place  in  inductive  and  de- 
ductive generalizations.  There  could  no  longer  be  any 
question  of  an  element  still  to  be  found  in  an  unexplored 
and  changing  complex. 

Nevertheless,  each  of  these  complexes,  with  confused 


132  Annals  of  the  American  Academy. 

and  unknown  elements,  would  have  certain  definite  char- 
acteristics as  an  entirety.  A  State,  a  country,  a  harbor,  a 
town,  a  section  of  the  heavens,  the  monthly  weather  of  a 
station,  and  so  forth,  have  all  general  qualities  that  char- 
acterize them  as  entireties,  so  that  other  entireties  falling 
in  the  same  categories  may  be  recognized.  According  to 
his  notion  a  human  being  is  known  as  an  individual,  but 
he  is  capable  of  conception  as  collective,  at  any  rate  as  an 
aggregate.  Numerous  more  or  less  changeable  elements 
are  to  be  observed  upon  him,  as  teeth,  eye-brows,  and 
freckles,  which,  for  a  medical  or  anthropological  purpose, 
might  be  subjected  to  a  statistical  enumeration  and  com- 
parison. 

The  idea,  therefore,  which  is  to  be  held  of  the  inves- 
tigated aggregate  as  an  entirety  determines  the  analogy 
with  other  aggregates.  Particular  attention  must  be  given 
to  the  elasticity  of  the  terms  used,  and  the  application 
of  very  different  notions  to  one  and  the  same  actual 
entirety. 

For  each  statistical  problem  the  aggregate  to  be  investi- 
gated can  be  conceived  only  in  a  single  way.  If  that  be 
changed  the  notion  of  the  aggregate  changes,  and  with  it 
the  problem.  What  are  apparently  two  identical  problems 
become  two  different  ones.  The  reverse  holds,  and  the 
change  of  the  problem  involves  a  change  in  the  notion  of 
the  whole.  If  it  be  asked  whether  Prussia  had  a  large 
growth  of  population  during  the  last  census  period,  the 
notion  of  the  aggregate  Prussia,  and  hence  of  all  analo- 
gous aggregates,  is  very  different,  according  as  the  ques- 
tion means,  was  the  growth  large  as  growth  or  large  for 
Prussia.  In  the  first  place,  Prussia  is  conceived  as  a  civil- 
ized country,  and  the  analogy  attaches  to  that  notion ;  but, 
in  the  second  case,  Prussia  is  conceived  with  all  its  peculi- 
arities, and  it  has  no  analogy  but  itself.  Here  the  task  is 
simply  to  compare  the  aggregates  of  Prussia  at  different 
census  periods  among  themselves. 

Now,  it  is  obvious  that  according  to  the  nature  of  the 


Theory  and  Technique  of  Statistics.  133 

problem  a  limited  group  of  aggregates,  instead  of  many, 
may  be  sufficient  to  furnish  a  standard  of  comparison.  It 
would  certainly  be  sufficient  in  the  first  case  to  compare 
Prussia  with  the  most  important  States  with  trustworthy 
statistics,  and  in  the  second  case  the  Prussian  figures  for 
the  last  three  or  four  decades. 

The  notion  under  which  an  aggregate  to  be  investigated 
may  be  conceived  for  comparison  may  vary  from  a  definite 
individual  to  a  part  of  concrete  existence,  limited  in  time 
and  space,  but  otherwise  wholly  unknown.  Hence  the 
choice  of  analogies  requires  acute  distinctions,  but  is 
always  possible.  It  is  questionable  how  far  comparison 
must  be  abandoned  because  an  enumeration  of  like  units 
in  analogous  aggregates  has  not  taken  place,  or  cannot  be 
effected. 

The  problems  of  practical  statistics  are  usually  those  for 
which  provision  for  comparison  can  be  readily  made  at  the 
time  of  enumeration,  or  already  exist  in  previous  results. 
If  these  problems  are  to  be  solved  within  the  limits  of  a 
single  country,  there  are,  as  a  rule,  a  great  number  of  com- 
parable aggregates  for  which  exactly  the  same  enumeration 
has  been  made.  We  have,  on  the  one  hand,  the  minor 
subdivisions  of  the  country,  as  provinces,  counties,  even  to 
townships,  which  are  distinguished  in  the  enumeration,  so 
that  each  division  is  a  separate  aggregate,  the  sum  of 
whose  units  may  be  compared  with  that  of  others.  On 
the  other  hand,  from  year  to  year,  or  at  definite  periods, 
certain  enumerations  are  made  where  like  units  are  counted 
in  the  various  subdivisions  of  the  country,  and  thus  a  new 
series  of  analogous  and  comparable  aggregates  is  obtained. 
For  such  questions  which  extend  beyond  the  limits  of 
one's  own  country,  there  are  means  of  solution  to  be  found. 
Most  civilized  States  undertake,  from  similar  necessities, 
similar  statistical  enumerations.  But  it  cannot  be  denied 
that  international  statistics  show  some  very  bad  gaps  and 
other  imperfections. 

They  are  not  caused  by  a  lack  of  analogies,  but  by  a 


134  Annals  of  the  American  Academy. 

lack  of  sufficient  agreement  in  units  of  enumeration.  Like 
names  for  things  counted  may  lead  one  to  overlook  that 
different  States  apply  the  same  designation  to  units  which 
are  different  for  purposes  of  comparisons,  because  unlike 
in  composition  and  origin.  (O.  Haussner,  Vergleichende 
Statistik  von  Europa,  1864.) 

Statistical  problems   are   always  incapable  of  solution 
/  /  when  it  is  impossible  to  find  a  basis  of  comparison  in 
analogous  aggregates  examined  with  reference  to  exactly 
the  same  units. 

§  76.    REDUCTION   TO    COMMON   TERMS. 

A  comparison  of  the  analogous  masses  is  not  attainable 
directly.  Some  basis  of  comparison  must  be  found  by 
reducing  the  results  to  common  terms.  This  reduction 
depends,  like  the  choice  of  the  units,  upon  the  nature  of 
the  problem. 

If  the  purpose  of  the  problem  is  to  determine  the  relative 
frequency  of  the  occurrence  of  the  phenomena,  the  com- 
mon terms  must  be  in  measures  of  time  and  space  for  the 
various  analogous  aggregates.  Hence  there  must  always 
//  be  an  equal  measure  of  time  and  space — thus,  for  1  square 
mile  in  1  year  x  wheat.  No  limitation  of  space  is  neces- 
sary when  the  aggregate  has  changed  in  time  only  and 
not  in  space  (Province  A,  1  year  y  taxes),  or,  when  in  an 
observation  of  movement,  the  place  is  a  point  from  which 
the  number  is  counted  (Canal  B,  1  week  z  vessels).  In 
like  manner  the  time  needs  no  limitation,  when  the  condi- 
) )  tion  in  all  parts  is  recorded  at  one  moment  (State  C,  1  sq. 
m.,  x  inhabitants,  y  houses,  z  arable  land).  In  all  these 
cases  time  and  space  are  bases  of  the  comparison. 

The  measurement  of  time  has  naturally  few  difficulties. 
On  the  contrary,  the  measurement  of  space  requires  often 
very  extensive  operations  of  survey  and  triangulation, 
which  statistics  are  not  in  a  position  to  carry  out.  It 
has  to  presuppose  the  existence  of  this,  and  expects  to  find 
it  completed,  just  as  much  as  the  measuring  of  the  qualities 


i 


Theory  and  Technique  of  Statistics.  135 

of  the  units.  The  survey  and  triangulation  of  territories, 
or  calculations  which  are  not  always  exact  from  the 
geographical  boundaries,  furnish  the  necessary  data  in  this 
matter. 

The  number  of  things  enumerated  for  each  common 
term  is  found  by  calculating  what  part  of  the  entire  aggre- 
gate it  forms.  The  same  proportion  of  the  total  number 
of  units  must  fall  upon  this  term.  Therefore,  for  these 
common  terms  the  most  various  units  can  be  shown  side 
by  side  with  all  their  distinctive  differences.  This  division 
of  the  total  is  simply  one  of  calculating  proportions,  and 
would  never  justify  the  conclusion  that  a  similar  distribu- 
tion in  the  density  of  units  occurs  in  the  real  parts  of  the 
field. 

As  the  aggregate  is  to  be  measured  by  mutual  relations 
of  the  units,  the  reduction  to  common  terms  takes  the  form 
of  the  reduction  of  various  units  to  an  equal  quantity  of  one 
unit,  and,  as  a  rule,  percentually  (for  100  units  A  there 
are  x  units  B).  Any  unit. can  be  used  for  this  purpose. 
Specifications  of  the  main  unit  are  hereby  rendered  much 
clearer  in  their  relations  to  the  central  idea.  Sometimes 
for  such  combinations  an  equal  period  of  time  must  also 
be  drawn  into  the  problem  (as  for  100  inhabitants  y  births 
in  1  year).  In  like  manner  a  restriction  of  place  may  be 
necessary.  But  here  the  percentual  number  expresses 
simply  an  average,  not  at  all  that  in  the  aggregate  or  its 
parts,  or  anywhere  in  particular,  for  100  units  A  there  are 
x  units  B  in  nearer  or  more  definite  relations.  The  reduc- 
tion to  common  terms  which  always  has  the  same  purpose, 
becomes  a  very  extended  calculation  when  it  deals  with 
many  distinctions  and  differently  graded  qualities.  (Ernte- 
statistik,  Bd.  I.  d.  Stat.  d.  Deutsch.  Reiches,  p.  1 10.) 

§  77.   SERIES,    MAXIMA,    MINIMA,   AND   AVERAGES. 

The  results  obtained  by  reducing  the  results  of  enumer- 
ation to  common  terms  always  furnishes  a  series  admitting 


136  Annals  of  the  American  Academy. 

of  comparison.  The  figures  for  the  same  unit  show  in 
which  aggregate  relatively  the  largest  and  in  which  the 
smallest  number  of  units  is  to  be  found.  Arranged  from 
minimum  to  maximum,  they  show  the  order  in  which  the 
degrees  of  intensity  progress.  Arranged  according  to 
the  geographical  position  of  the  masses,  they  show  the 
intensity  in  its  distribution,  and  arranged  by  their  succes- 
sion in  time,  the  fluctuation  of  their  historical  development. 

The  fluctuation  appears  either  as  regular  growth  or  de- 
crease, or  as  an  oscillation  which,  though  changing,  returns 
to  similar  maxima  and  minima. 

Two  or  more  such  series  placed  beside  each  other,  and 
thus  showing  a  comparison  of  different  units,  may  be  ex- 
amined as  to  the  similarity  or  dissimilarity  of  their  courses, 
whether  they  oscillate  in  the  same  or  opposite  directions, 
and  whether  the  maxima  occur  positively  or  negatively  at 
the  same  point  of  the  series  or  not.     (Compare  Appendix 

mo 

For  the  fluctuations  of  a  single  series  we  find  the  measure 
\  J  in  the  average.  The  average  expresses  the  mean  figure, 
^the  mean  importance  of  all  the  fluctuations  of  the  series, 
so  that  the  individual  figures  extend  beyond  it,  some  nega- 
tively, some  positively,  in  equal  proportions.  The  average 
cannot  be  gained  immediately  from  the  series  itself.  It 
must  give  the  mean  value  of  the  totals  of  all  the  aggregates, 
and  cannot,  therefore,  be  calculated  from  the  ratios,  but 
only  from  the  absolute  figures,  the  sum  of  all  the  units  of 
enumeration  of  all  the  aggregates  compared,  divided  by 
the  sum  of  all  the  quantities  used  for  the  reduction  to 
common  terms.  For  the  comparison  of  several  series, 
there  must  be  an  average  for  each  to  serve  as  a  basis  of 
comparison.  (Lexis,  quoted  §  16,  and  Marey,  quoted  §  57.) 

§  78.  results  from  quantitative  judgments. 

From  such  series  of  relative  numbers  we  can  form  a 
quantitative  judgment,  that  is  to  say,  a  conclusion  as  to 


Theory  and  Technique  of  Statistics.  137 

the  greater  or  lesser  measure  in  which  the  things  deter- 
mined upon  as  units  of  enumeration  are  present  in  the 
aggregate  investigated. 

The  more  numerous  the  series  the  clearer  is  our  insight 
into  the  subject,  since  we  know  the  relations  of  a  larger 
number  of  component  things.  And  the  more  varied  the 
relations  among  the  things  are,  their  grouping  as  genera 
and  species,  as  well  as  other  relations,  the  greater  is  the 
definiteness  which  the  aggregate  assumes.  We  also  know 
in  what  relations  these  things  occur  in  other  aggregates, 
which,  however  variable,  may  be  regarded  when  considered 
as  units  as  belonging  to  the  same  class  as  the  aggregate 
which  has  been  investigated. 

The  things  themselves  are  not  examined.  We  find  \\ 
simply  the  frequency  of  their  occurrence,  their  quantita- 
tive distribution  in  certain  limits  of  time  and  space, 
among  other  things  which  remain  unknown,  but  which 
fill  out  the  space.  Thus  a  certain  general  measure  of 
their  mutual  relations  is  determined,  in  a  somewhat  sum- 
mary manner,  it  is  true,  but  in  one  not  to  be  reached  by 
other  methods. 

Thus  the  aggregates  themselves  are  better  known  and 
are  more  capable  of  comparison.  As  they  agree  in  those 
essential  items  which  characterize  them  as  individuals  or 
as  collectives,  it  is  very  important  to  find  that  other  ele- 
ments, which  appear  fluctuating  and  unstable,  can  be 
measured,  at  least  as  to  their  intensity  and  probable 
mutual  relations,  by  definite  measures,  and  in  relation  to 
similar  aggregates. 

Thus  the  first  step  of  statistical  judgment,  i.  e.}  the  judg- 
ment of  quantitative  relations,  is  complete.  It  is  the  indis-  » 
pensable  basis  of  any  further  progress.  By  far  the  greater 
part  of  the  statistical  activity  whose  results  reach  the  public 
and  become  common  property,  does  not  go  further  than 
this  first  step  in  the  knowledge  to  be  gained  from  statistical 
enumerations.  Ponderous  statistical  publications  of  official 
bureaus  deal  in  the  main  with  this  class  of  description.     It 


138  Annals  of  the  American  Academy. 

is  rarely  that  an  investigation  steps  beyond  the  limits  of 
this  quantitative  judgment.  This  is  all  the  more  explain- 
able, as  this  is  the  field  in  which,  as  much  as  possible  for 
empirical  knowledge,  exact  results  and  conclusions  may 
be  reached. 

All  further  conclusions  based  upon  these  results,  as- 
sume unavoidably  a  more  or  less  hypothetical  character. 
Nevertheless,  it  would  be  quite  impossible  to  confine  sta- 
tistical investigations  to  quantitative  judgments,  even  if 
we  should  follow  the  most  restricted  conception  of  the 
limits  of  statistical  science.  The  final  and  conclusive 
utility  of  this  primary  requisite  of  methodical  statistical 
investigation  is  certainly  not  to  be  found  in  the  rich  mate- 
rials that  it  presents,  but  in  the  conclusions  to  be  drawn 
from  them. 

II.  Causal  Connections. 

§  79.   REQUIREMENTS    AND    LIMITATIONS    OF   JUDGMENTS 
OF   CAUSALITY. 

The  next  step  in  statistical  investigation  after  the  details 
of  the  quantitative  relations  must  be  an  effort  to  explain 
the  reasons  for  the  numerical  relations  which  have  been 
discovered ;  in  short,  their  relations  of  cause  and  effect. 
It  is  in  the  nature  of  our  reasoning  to  suppose  a  cause  for 
every  effect,  and  to  seek  to  find  it.  All  phenomena  are 
subject  to  the  rule.  For  every  phenomenon  we  think  at 
once  of  a  cause  and  try  to  find  it ;  or,  in  other  words,  we 
seek  a  satisfactory  explanation  of  the  phenomenon.  While 
our  perceptions  have  the  form  of  descriptions,  the  interest 
we  take  in  them  is  the  effort  to  determine  causality. 

To  demonstrate  the  causes  empirically  is  very  difficult. 
We  are  conscious  of  causes  only  in  our  own  actions. 
In  the  external  world  they  appear  only  as  succession  in 
time,  and  whether  A  is  the  cause  of  B,  which  follows  it  in 
point  of  time,  cannot  be  maintained  without  danger  of  error. 


Theory  and  Technique  of  Statistics.  139 

For  individual  cases,  therefore,  the  proof  is  carried  out  by 
experiment.  The  object  is  placed  successively  under  one 
influence  to  the  exclusion  of  all  others,  and  the  conse- 
quences observed,  until  it  appears  which  influence  brings 
about  the  effect. 

Statistics  can  make  no  such  experiment  with  the  phe- 
nomena of  aggregates  with  v/hich  it  deals.  In  the  com- 
plex aggregate  the  most  varied  and  opposite  causes  must 
always  be  at  work.  Statistical  methods  cannot  expect  a 
knowledge  of  all  the  things  in  the  aggregate,  and  cannot, 
therefore,  attempt  an  investigation  of  all  the  causes  in 
operation.  In  the  judgment  of  causal  connection,  it  is 
limited  to  certain  phenomena,  the  frequency  of  whose 
occurrence  has  been  numerically  measured.  It  can  only 
ask  what  causes  have  produced  these  relations,  or  what 
effect  may  be  traced  to  them. 

The  process  by  which  the  answer  is  made  resembles 
somewhat  that  of  experiment.  We  take  up  in  succession 
the  possible  causes.  We  may  suppose,  at  first,  the  most 
probable  to  be  actually  operative,  and  look  for  indications 
whether  or  not  this  is  the  case.  If  not,  each  probable 
cause  must  be  examined  successively,  until  one  appears 
to  be  sufficiently  well  founded.  If  the  supposed  causes 
are  exhausted  without  success,  then  there  remains  simply 
the  same  result  as  in  a  fruitless  experiment,  that,  of  all 
conceivable  causes,  none  seem  to  be  at  work. 

§  80.    DISCOVERY   OF   CAUSALITY   THROUGH    FUNCTIONAL 
SERIES. 

Statistical  methods  can  only  look  for  indications  of  the 
causal  connections  of  two  phenomena,  in  the  mutual  rela- 
tions of  the  quantities  in  which  they  are  found.  Their 
frequency  in  the  aggregate  investigated  is  not  alone  suffi- 
cient for  a  demonstration. 

This  is  expressed  by  two  figures  which  are  otherwise 
unrelated.     For  any  judgment  as  to  the  meaning  of  these 


140  Annals  of  the  American  Academy. 

figures  it  is  indispensable  to  compare  the  figures  which 
have  been  observed  within  a  group  of  analogous  aggre- 
gates for  the  same  units. 
1/  Since  the  cause  produces  the  effect,  the  cause  and  effect 
must  be  weaker  or  stronger  together.  Whether  an  increase 
in  the  intensity  of  the  cause  shows  itself  positively  or 
negatively  is  indifferent.  Our  idea  of  a  sufficient  cause  is 
based  upon  its  functional  relation  to  the  effect. 

The  proof  of  causality  can  only  be  given  in  the  course 
of  two  series  of  relative  numbers  :  one  which  shows  the 
measure  of  the  cause,  the  other  the  measure  of  the  effect, 
in  the  aggregates  compared.  If  the  effect  A  is  really  the 
result  of  the  cause  B,  the  relative  number  of  the  units  A 
must  in  all  these  aggregates  vary  in  the  same  or  opposite 
ratio  as  that  of  the  units  B. 

But  if  such  a  relation,  with  the  exception  of  such  devia- 
tions as  may  be  explained,  does  not  appear,  the  supposition 
of  causality  is  to  be  rejected.  On  the  other  hand,  the 
agreement  of  two  series  is  not  to  be  considered  an  abso- 
lute demonstration  of  the  causal  connection  of  the  phe- 
nomena. It  is  only  a  presumption  of  such  a  connection. 
Both  may  be  the  effects  of  the  same  cause,  or,  indeed, 
numerous  combinations  of  the  most  divergent  causes 
might  lead  to  a  similar  final  resultant  in  each  series. 

Hence,  to  decide  as  to  the  nature  of  connection  between 
agreeing  series  we  require  still  further  evidence. 

Such  evidence  can  be  found,  as  in  the  choice  of  analo- 
gous masses,  only  by  the  use  of  knowledge  which  has 
//been  gained  by  the  inductive  processes  of  experiment  and 
'  observation.  Numerous  causal  connections  between  single 
things,  individual  as  well  as  collective,  are  sufficiently  well 
grounded  to  be  generally  known.  From  such  knowledge 
one  may  by  induction  or  deduction  presume  the  effect  of 
a  given  cause  which  is  the  most  immediate  and  prob- 
able. 

In  order  to  know  the  cause  whose  effect  is  expressed  in 
the  series  A  we  must  fix  our  attention  upon  the  cause  Z, 


Appendix  III.   (to  §  80). 


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Theory  and  Technique  of  Statistics.  141 

which  inductive  knowledge  tells  us  is  the  most  immediate 
cause  of  which  A  is  the  effect.  We  then  note  the  series 
of  the  phenomenon  Z  in  all  the  analogous  aggregates  to 
be  compared.  If  the  series  Z  is  present  among  the  enu- 
merated units,  it  is  easy  to  decide  whether  the  functional 
relation  of  the  two  series  permits  us  to  suppose  a  causal 
connection  in  the  case.  If  the  series  Z  has  not  been 
counted,  this  must  take  place,  or  a  sufficient  substitute, 
which  can  take  the  place  of  the  series  Z,  be  gathered  from 
the  enumeration. 

If  it  appears  that  no  functional  relation  exists  between 
the  two  series  we  cannot  assume  this  cause  to  be  of  influ- 
ence, even  though  under  ordinary  circumstances  it  may  be 
the  most  probable.  We  must  rather  look  for  the  cause  Y, 
next  in  order  of  probability,  and  apply  to  it  the  same 
process,  and  so  the  successive  probable  causes,  X,  W,  V,  T, 
etc.  Thus  we  continue  until  we  find  a  correspondence 
between  the  series  with  one  of  the  causes,  or  else  we  must 
abandon  the  hope  of  establishing  the  real  cause  from 
among  the  probable  ones  which  we  know.  In  this  case 
the  negative  result  is  undoubtedly  of  great  value.  All 
presumptions  are  cut  off  which  seemed  most  reasonable, 
and  this  negation  may  serve  for  the  solution  of  exceedingly 
important  problems. 

The  result  may  be  that  another  series,  B,  which  no  one 
supposed  to  be  connected  with  the  causes,  is  now  found  to 
be  important  through  excluding  the  seemingly  more  imme- 
diate causes.  It  may  be  apparently  improbable  and  diffi- 
cult of  comprehension,  but  must,  when  all  other  connec- 
tions fail,  be  recognized  as  the  fact  in  which  the  forces  at 
work  find  a  clear  expression.  An  example  is  given  in 
Appendix  III.:  marriages  and  the  prices  of  rye. 


// 


142  Annals  of  the  American  Academy. 

§8l.  symptoms  and  their  application   in   determining 

causality. 

In  finding  an  explanation  of  cause  and  effect  we  do  not 
have  all  the  elements  of  the  solution  in  the  problem  itself, 
as  in  the  case  of  the  quantitative  relations  of  the  phe- 
nomena. 

The  necessity  of  introducing  certain  phenomena  for 
comparison  appears  in  the  course  of  the  proof.  The  in- 
vestigation of  causality  does  not  look  for  the  scattered  and 
characteristic  features  of  a  picture,  but  the  confirmation  of 
a  chain  of  more  or  less  obvious  or  obscure  conjectures, 
none  of  which  can  be  disregarded  without  fear  of  error. 
It  is  purely  a  happy  accident  if  all  the  figures  necessary 
for  the  comparison  are  in  existence  or  can  be  obtained. 
In  case  no  enumerations  have  been  made  for  analogous 
aggregates  of  units  essential  to  the  proof,  or  are  wholly 
impracticable,  something  else  must,  as  pointed  out  in  §62, 
take  their  place.  We  thus  arrive  at  the  question  of  so- 
called  symptoms. 

These  symptoms  are  indications,  but  they  cannot,  as 
demonstrated  by  §65,  be  found  in  qualities  or  abstrac- 
tions from  conditions.  Statistical  methods  cannot  say  that 
things  (money,  capital)  are  symptoms  of  qualities  (rich), 
or  of  abstractions  from  this  quality  (riches).  Only  per- 
sons can  be  rich ;  whether  they  are  rich  and  in  what 
degree  can  only  be  determined  in  considering  persons,  and 
to  say  what  capital  constitutes  riches,  makes  sense  only  in 
connection  with  persons.  Capital  expressed  in  money 
can  be  counted,  but  it  shows  riches  only  in  the  relative 
possessions  of  persons. 

A  symptom  means  in  statistics  something  capable  of 
enumeration,  which  shows  by  its  number  that  something 
may  be  inferred  in  a  corresponding  number,  or  one  to  be 
estimated  or  calculated.  For  different  degrees  of  rich  per- 
sons, whom  it  would  be  very  difficult  to  count,  we  find  a 
symptom  in  the  returns  of  persons  liable  for  income  or 


Theory  and  Technique  of  Statistics.  143 

property  taxes.  In  the  statistical  inquiry  as  to  causality 
one  of  the  most  important  problems  is  the  choice  of  these 
symptoms.  Gioja  (see  §  46)  called  attention  to  this  in  an 
instructive  way. 

On  the  other  hand,  there  are  no  general  rules  for  the 
proper  choice  and  use  of  symptoms.  One  thing  can  never 
be  replaced  exactly  by  another.  The  acuteness  of  the  judg- 
ment must  suffer  in  some  degree.  At  the  same  time  the 
application  of  the  theoretically  best  symptom  is  oftentimes 
quite  as  impossible  as  the  use  of  direct  results  of  enumera- 
tion. A  suitable  choice  must  remain  a  matter  of  a  clear 
and  keen  conception  of  the  special  problem,  and  of  all  the 
resources  which  may  be  drawn  upon  for  its  solution. 

Some  misgiving  may  arise  from  the  need  of  symptoms, 
but  it  cannot  be  overlooked  that  they  bring  an  important 
element  of  flexibility  and  variety  into  the  methods  of  sta- 
tistics. By  means  of  one  unit  replacing  another  the  results 
of  enumeration  may  be  utilized  for  conclusions,  which 
would  have  required  in  the  original  problem  or  in  others 
an  enumeration  under  totally  different  circumstances. 

III.  Probability  and  Regularity. 

§  82.  the  conception  of  probability. 

The  hypothetical  demonstration  of  causal  connections 
in  statistical  aggregates  furnishes  the  basis  for  the  solution 
of  a  vast  number  of  practical  and  scientific  problems.  It 
is,  moreover,  indirectly  of  peculiar  significance  for  statist 
tical  methods.  (The  insight  into  causal  connections  ren~ 
ders  possible  a  judgment  of  probabilities  and  the  expecta- 
tion of  regularities. 

This  further  step  in  statistical  knowledge  opens  up  a 
wide  possibility  of  solving  many  problems,  even  quite 
complicated  ones.  By  its  means  conclusions  may  be 
formed  as  to  the  quantities  in  which  qualities,  which  have 
not  been  enumerated,  are  to  be  found  in  the  aggregate  to 


144  Annals  of  the  American  Academy. 

be  investigated,  and  which  may,  therefore,  be  expected 
with  adequate  regularity  in  similar  aggregates.  What  we 
know  as  probability  is  based  upon  the  idea  that  what 
occurs  regularly  in  our  experience  under  certain  circum- 
stances is  very  likely  to  occur  again  in  the  same  way 
if  the  circumstances  do  not  change.  Phenomena  which 
have  been  demonstrated  to  be  the  result  of  a  certain  com- 
bination of  circumstances,  even  though  some  are  not 
.  wholly  known,  may  be  expected  with  greater  probability 
than  any  other  phenomena  from  the  same  combination. 
This  line  of  thought  is  distinctively  causal.  The  cir- 
cumstances are  the  causes,  which  being  uniform  must 
produce  uniform  effects.  If  the  circumstances  cannot  by 
any  possibility  change,  and  permit  only  a  limited  series 
of  possible  results,  a  calculation  may  be  made  of  the 
degree  of  probability  of  each  of  these  results.  This  is 
the  idea  of  the  calculation  of  games  of  chance,  and  of 
Bernouilli's  principle  of  Probability  (§  15). 

This  principle  is  expressed  as  follows :  "  If  a  large  num- 
ber of  cases  have  been  observed  of  several  events  which 
have  a  certain  probability,  the  number  of  cases  in  which 
each  event  has  occurred  will  approach  very  closely  to  its 
probability,  and  this  more  and  more  precisely  the  more 
extended  the  number  of  observations."  Bernouilli,  how- 
ever, limits  this  rule,  inasmuch  as  when  the  number  of 
possible  events  is  infinitely  great,  that  is,  when  the  num- 
ber of  events  is  not  limited,  but  may  expand  indefinitely, 
the  principle  does  not  hold.  In  many  statistical  problems, 
as  in  the  calculation  of  death  tables,  the  series  of  possible 
cases  may  be  regarded  as  complete,  on  account  of  the  in- 
finitesimal number  of  those  dying  at  very  advanced  ages, 
and  Bernouilli's  principle  may  be  considered  applicable. 

As  a  rule,  however,  the  form  of  the  calculation  of  prob- 
abilities, as  applied  by  statistical  methods,  undergoes  a 
two-fold  modification.  On  the  one  hand,  it  results  from 
the  nature  of  the  aggregates  to  be  investigated,  that  they 
include   an   infinitely  great   number  of  different  possible 


Theory  and  Technique  of  Statistics.  145 

phenomena.  On  the  other  hand,  it  is  only  exceptionally 
that  statistical  problems  require  the  degree  of  probability 
of  a  certain  phenomena,  but  rather  in  what  quantity  or 
what  relation  a  certain  phenomena  may  be  expected.  This 
is  a  reversal  of  the  problem  which  simplifies  it,  and  ren- 
ders less  important  the  lack  of  a  definite  limitation  of  the 
phenomena. 

In  all  cases  it  is  clear  that  a  large  series  of  aggregates 
is  much  more  likely  to  comprehend  all  the  possibilities  of 
the  occurrence  of  a  phenomena  than  a  small  series.  It  is, 
nevertheless,  just  as  little  to  be  doubted  that  without  limi- 
tation even  the  largest  series  does  not  give  any  absolute 
security  that  all  possibilities  are  actually  contained  in  it. 

In  order,  therefore,  to  obtain  a  definite  numerical  ex- 
pression  by   a   calculation  of  probability   instead  of  by  . 
enumeration,  statistics  must  make  use  of  a  fiction.     This 
fiction  expressed  in  logical  terms  is  that  in  the  series  of 
enumerated   aggregates  which  are  compared,  the   possi-  * 
bilities   in    question    are   to   be   regarded   as   exhausted. 
Actually  this   supposition  has  a  concrete  justification  in 
the  fact  shown  in  §  75,  that  the  analogous  aggregates  are 
chosen  with  knowledge  of  and  reference  to  their  peculi- 
arities.    Statistical  problems  employ  this  fiction  so  exten- 
sively that  the  sphere  of  comparison  becomes  frequently 
very  narrow.     In  case  of  necessity  the  probability  is  often  . 
judged  from  the  results  of  a  single  enumeration;  i.  e.,  the 
possible  variation  is  estimated. 

But,  as  a  matter  of  fact,  the  difficulties  and  the  interest 
of  these  problems  do  not  hinge  so  much  on  the  questions, 
which  cases  are  possible,  and  hence  may  interfere  with 
the  action  supposed,  but  they  rest  on  the  doubt  whether 
known  possibilities  have  been  correctly  judged  in  their  I 
causal  connections. 


146  Annals  of  the  American  Academy. 

§  83.  suppositions  based  on  similar  causality. 

The  process  of  assuming  by  probabilities  the  number  of 
things  which  have  not  been  counted  is  based  wholly  upon 
the  idea  explained  in  the  foregoing  section,  that  in  the  ag- 
gregate to  be  investigated  the  same  causes  operate  as  in  . 
the  analogous  aggregates.  Like  numerical  relations  under 
dissimilar  conditions  would  be  highly  improbable.  These 
conditions  of  the  conclusion  as  to  probability  cannot  but 
exert  an  influence  upon  the  choice  of  analogous  aggre- 
gates. The  analogy  of  the  aggregates  is  determined  by 
the  same  conception,  be  it  broad  or  narrow,  of  them  as 
entireties,  either  individual  or  collective,  presupposing 
always  that  the  distinctions  have  been  drawn  with  care 
and  attention.  Whether  or  not  the  analogous  aggregates 
have  actually  been  subject  to  such  similar  circumstances, 
that  the  causes  at  work  from  which  the  probable  figure  is 
deduced  have  been  actually  identical,  is  one  of  those  ques- 
tions for  whose  answer  statistics  must  draw  upon  general 
empirical  knowledge.  Here  it  is  necessary  to  consider, 
according  to  the  nature  of  the  problem,  the  different 
influences  which  may  be  at  work  in  contemporary  his- 
tory, in  political  or  economic  life,  and  in  the  processes 
of  nature.  » 

Such  influences  may  often  be  determined  statistically, 
and  be  observed  in  the  search  for  cause  and  effect. 
Whether  this  takes  place  depends  largely  on  the  time 
and  cost  involved,  and  on  the  importance  attached  to  the 
question.  Influences  which  are  generally  operative  are  to 
be  regarded  as  causes,  since  they  affect  the  relations  of  the 
parts  to  the  whole  in  the  same  way  in  all  cases.  When  it 
is  known  that  influences  are  at  work  whose  effects  are 
partial  only,  the  aggregates  in  which  they  occur  must 
be  withdrawn  from  the  examination.  For  it  is  preferable 
to  know  positively  that  like  conditions  exist  among  the 
aggregates  compared  than  to  extend  the  comparison  to 
a  great  number  of  them. 


Theory  and  Technique  of  Statistics.  147 

In  all  events  no  effort  should  be  spared  to  ascertain 
whether  special  influences  have  been  at  work  in  some  of 
the  aggregates  considered  as  analogous,  or  indeed  whether 
the  aggregate  to  be  investigated  has  not  been  subjected  to 
some  unknown  influence,  which  would  render  unreliable 
any  conclusion  upon  the  basis  of  probabilities. 

Nevertheless  it  would  not  answer  to  indicate  these  pos- 
sibilities of  error  by  expressing  the  probability  in  hypo- 
thetical or  indefinite  numbers.  The  probability  would  be 
useless  for  any  scientific  purpose  by  such  uncertainty.  On 
the  contrary,  any  doubts  as  to  the  certainty  of  the  result 
must  find  expression  with  sufficient  explanation  in  a  critical 
examination  of  the  margin  of  error. 

Employing  the  fiction  already  named,  that  the  aggre- 
gates compared  exhaust  all  the  possibilities  to  be  con- 
sidered, it  is  an  easy  matter  to  obtain  the  most  probable 
number.  In  one  case  the  desired  phenomena  has  not 
been  counted  in  the  aggregate  to  be  investigated,  but  in 
the  analogous  aggregates,  whereas  the  series  of  causes  or 
effects  corresponding  to  this  phenomena  have  been  enu- 
merated in  all.  Here  the  phenomena  in  question  will 
bear  the  same  relation  in  this  series  in  the  aggregates  to 
be  investigated  as  it  does  on  an  average  in  the  analogous 
ones.  In  another  case  the  series  of  causes  and  effects  have 
not  been  determined  for  the  aggregate  under  investigation, 
but  it  is  supposed  that  like  circumstances  affect  this  and 
the  analogous  aggregates.  Here  the  desired  result  would 
be  the  average  of  the  analogous  aggregates  reduced  to  an 
equal  size  with  that  investigated. 

When  a  series  of  enumerations  for  analogous  aggregates 
is  at  our  disposal,  and  the  probability  may  be  calculated 
from  their  average,  it  seems  advisable  to  note  the  possible 
deviation  of  the  actual  number  from  this  average.  In  the 
most  extreme  case  the  deviation  can  be  supposed  to  equal 
the  actual  extremes  in  the  series.  When,  however,  we 
desire  to  find  the  probable  deviation  on  one  side  or  the 


143  Annals  of  the  American  Academy. 

other,  we  can  calculate  the  mean  of  the  deviations  from 
the  average  on  each  side. 

The  extensive  application  of  probabilities  has  led  to  cer- 
tain points  of  view  which  require  more  precise  explanation, 
and  a  correct  estimate  of  their  relations  to  the  whole  field 
of  probability.  They  are  the  so-called  law  of  large  num- 
bers and  the  so-called  regularity  of  seemingly  voluntary 
actions. 


§  84.   THE  SO-CALLED   LAW  OF  LARGE  NUMBERS. 

The  so-called  law  of  large  numbers  has  often  been 
treated  as  some  mysterious  force  peculiar  to  large  aggre- 
gates, through  which  large  numbers  establish  regularity. 
The  conception  is  more  correct,  that  in  a  large  number 
the  actual  relations  are  more  accurately  expressed  than  in 
a  small  number,  and  hence  probability  may  be  concluded 
much  more  safely  from  a  large  number. 

If  there  were  any  necessity  for  the  phenomena  found  in 
large  numbers,  it  would  be  equally  well  expressed  in  the 
small  ones.  And  if  this  necessity  were  recognized,  it 
might  indeed  be  developed  analytically  and  its  results 
calculated.  But  this  is  not  the  case.  The  reason  why 
the  character  of  an  aggregate  and  the  circumstances  at 
work  in  it  are  determined  more  readily  from  a  large 
number  of  phenomena  than  from  few  observations,  is 
simple.  Every  aggregate  is  composed  of  various  things, 
and  with  general  uniformity  there  may  still  be  some  ex- 
ceptional irregularities.  If  a  small  number  of  phenomena, 
that  is,  a  portion  of  the  aggregate  only,  is  considered,  it 
cannot  be  estimated  whether  accidental  exceptions,  causes 
of  error,  and  unusual  influences  may  not  be.  entirely  lack- 
ing or  especially  concentrated  in  this  portion,  and  hence 
any  conclusions  from  it  as  to  the  erroneous  nature  of 
the  whole.  In  a  large  number  such  exceptions  must  ap- 
pear in  nearly  the  same  relations  as  in  the  entire  aggre- 
gates.     A  single    case  can   only  be   either  regular  or 


Theory  and  Technique  of  Statistics.  149 

exceptional,  while  in  the  whole  regularities  and  exceptions 
assume  their  proper  proportions.  A  large  part  approaches 
the  whole  much  closer  than  a  small  one. 

In  a  derivative  sense  this  might  be  called  a  law,  because 
it  is  a  truth  uniform  under  all  conditions,  and  a  rule  for 
the  judgment  of  probability.  But  the  rule  has  obviously 
no  connection  with  the  relations  of  the  facts  themselves, 
but  only  with  the  formal  process  of  determining  them. 
The  phenomena  and  their  effects  occur  in  the  same  way 
whether  few  or  many  are  observed.  The  law  of  large 
numbers  has  no  more  influence  upon  the  facts  than  enu- 
meration itself.  It  is  not  a  rule  of  causality,  but  simply  a 
rule  of  perception. 

§85.    THE    REGULARITY   OF   SEEMINGLY   VOLUNTARY 
ACTIONS. 

The  doctrine  of  the  regularity  of  the  seemingly  volun- 
tary actions  was  formulated  by  Condorcet,  and  has  exercised 
an  important  influence  upon  the  theory  of  statistics  since 
the  time  of  Quetelet  (§51).  It  is  based  upon  the  fact  that 
certain  groups  of  human  actions  dependent  upon  the  will 
show  approximately  the  same  numerical  relations  in  their 
distribution  in  time  and  space.  On  this  basis  there  has 
been  postulated  more  or  less  emphatically  a  law  governing 
with  constraining  force  the  will  of  man.  In  its  elaboration 
this  has  led  to  the  idea  of  laws  ruling  the  entire  historical 
development  of  the  human  race,  capable  of  the  same  cal- 
culation as  those  governing  inanimate  matter.  With  this 
in  view,  some  have  broadly  denied  human  liberty  and 
moral  responsibility,  while  others  have  admitted  the  free- 
dom of  the  will  for  individuals,  but  denied  it  for  large 
groups  of  human  beings. 

A  law  governing  the  will  is  in  fact  incompatible  with 
responsibility  to  the  individual  conscience,  or  toward  one's 
fellow-creatures  or  the  State.  Such  a  law  would  dissolve 
all  religious  convictions,  the  State  and  civil  law.     It  must 


150  Annals  of  the  American  Academy. 

either  conform  to  the  laws  of  the  State,  in  which  case  the 
laws  would  be  obeyed  without  being  upon  the  statute 
books ;  or  it  must  be  contrary  to  those  laws,  and  in  this 
case  they  would  be  brushed  aside,  but  without  criminality 
or  redress. 

Whether  or  not  such  a  position  is  admissible  from  an 
ethical,  psychological,  or  anthropological  point  of  view, 
cannot  be  decisive  for  statistical  theory.  If  it  were  prova- 
ble by  statistical  means,  the  theory  of  statistics  would  have 
to  be  shaped  in  accordance  with  so  weighty  a  fact.  No  end 
could  be  more  worthy  of  statistics  than  to  prove  by  its 
critical  methods  a  definite  cosmological  system. 

An  investigation  of  the  facts  shows,  however,  in  the  first 
instance  that  such  uniformity  of  the  numerical  relations 
as  would  justify  the  conclusion  of  a  constraining  law  can- 
not be  conceded.  Suicides,  which  are  looked  upon  as 
the  most  decisive  proof  of  the  law,  have,  between  1836- 
1875,  in  quinquennial  periods,  varied  per  100,000  inhabit- 
ants as  follows:  Belgium,  3.65-7.01;  Austria,  4.60-1 1.93; 
Germany,  4.83-9.16;  England,  5.57-6.69;  Sweden,  5.66- 
8.49;  Norway,  7.33-10.90;  France,  7.62-14.55;  Prussia, 
10.28-13.28;  Saxony,  16.00-28.10;  Denmark,  21.40-28.60. 
If  from  these  figures  it  is  deduced  that  among  100, OOO 
inhabitants  100,000  suicides  would  have  been  possible, 
and  only  3.65-28.60  have  occurred,  this  would  be  a  rea- 
sonable approximation.  But  if  it  is  to  be  formulated  as  a 
law  that  among  100,000  inhabitants  3.65-28.60  must  com- 
mit suicide,  we  cannot  accord  our  assent.  Even  if  in  each 
State  only  the  given  figures  were  used,  and  the  minima 
and  maxima  represented  always  a  steady  progression,  and 
not  ups  and  downs,  there  could  be  no  conclusion  of  con- 
straining force.  This  becomes  more  and  more  evident  in 
comparing  lesser  areas  and  periods. 

Similar  results  are  to  be  obtained  from  a  detailed  examin- 
ation of  the  other  means  of  proof,  which  relate  chiefly  to 
the  illegitimate  births  and  various  kinds  of  criminals. 

The  motives  of  the  actions  whose  voluntary  character 


Theory  and  Technique  of  Statistics.  151 

has  been  questioned  are  in  most  cases  known  or  capable 
of  determination.  They  are  fully  conscious,  and  often 
contradictory,  according  to  changing  circumstances  and 
situations  of  the  persons.  Certain  motives  of  suicide  and 
crimes,  and  also  certain  modes  of  carrying  them  into 
execution,  increase  with  good  or  ill  fortune,  necessity  or 
plenty,  the  quiet  or  disturbance  of  contemporary  events. 

A  law  with  different  causes  cannot  be  a  natural  law. 
The  force  of  a  natural  law  is  permanently  and  uniformly 
inherent  in  all  natural  bodies.  Its  effects  may  be  rendered 
difficult  of  perception  by  the  action  of  opposing  forces, 
but  they  cannot  be  changed.  A  law  of  nature  cannot  affect 
the  aggregates  and  not  the  individual ;  it  works  uncondi- 
tionally in  each  individual  and  in  the  aggregate  only  by 
virtue  of  this  fact.  Death  is  based  upon  a  law  of  nature, 
and  possibly  also  the  fact  that  twenty-one  boys  are  born 
for  every  twenty  girls.  But  the  natural  law  must  be 
operative  in  every  death  and  every  birth,  and  not  simply 
in  a  certain  number  of  cases. 

Not  a  law  of  constraining  force,  but  simply  a  similar 
combination  of  many  and  varying  causes,  is  the  reason  for 
the  approximately  similar  phenomena.  But  this  basis  is 
insufficient  to  support  a  doubt  as  to  the  existence  of  the 
freedom  of  the  will.  The  expression  is  unhappily  chosen, 
for  the  act  of  willing  is  always  conceived  as  free.  If  ex- 
ternal law  controlled  without  opposition  the  will  of  man, 
his  existence  as  a  rational  being  must  cease.  Numbers 
do  not  control  his  will  but  only  his  action.  No  one  has 
claimed  for  man  entire  freedom  of  action.  The  sphere  of  /  / 
free  action  is  always  very  narrow.  It  is  limited  by  multi- 
fold external  circumstances,  by  the  power  of  environment, 
by  individuals,  by  the  State,  by  nature,  as  well  as  by  the 
powers  and  means  of  the  individual  himself.  But  for  free 
and  responsible  choice  a  broad  field  in  the  wide  possibility 
of  decision  remains  open.  The  scope  of  the  latter  is  shown 
not  only  by  the  difference  between  submitting  to  another's 
will  and  preferring  to  destroy  one's  own  existence,  but 


152  Annals  of  the  American  Academy. 

also  in  the  inexhaustible  modifications  in  the  mode  of  exe- 
cution and  the  ethical  value  of  actions  which  differ  but 
slightly. 

Finally,  it  cannot  be  overlooked  that  all  the  figures 
relied  upon  to  overthrow  the  freedom  of  the  will  are 
drawn  from  civilized  peoples.  These  live  under  like 
conditions,  and  it  is  not  remarkable  that  there  should 
here  appear  a  similarity  of  the  spontaneous  actions  of 
individuals. 

In  itself  human  nature  includes  the  uniformity  of  body 
and  mind  of  the  species  ;  in  civilized  States  there  are  added 
similar  classes  of  population,  similar  distribution  of  occu- 
pations, of  education,  and  of  income,  similar  principles  of 
law  and  administration,  similar  protection,  and  similar 
perils ;  and  within  the  like  classes,  like  views  of  life,  like 
needs,  like  pleasures,  and  like  habits. 

It  cannot  be  disputed  that  under  all  these  similar  con- 
ditions like  phenomena  are  more  probable  than  unlike, 
and  hence  great  disparity  would  appear  according  to  all 
presumptions  much  more  inexplicable  than  the  existing 
uniformity  with  its  slight  variations.  These  approximat- 
ing results,  which  vary  slightly  according  to  the  circum- 
stances, appear  much  more  natural  as  the  result  of  the 
liberty  of  the  will  than  as  a  consequence  of  constraining 
law. 

Statistics  finds  within  its  own  limits  a  satisfactory  ex- 
planation of  existing  regularities,  and  does  not  need  to 
borrow  metaphysical  or  materialistic  premises.  On  the 
contrary,  it  appears  that  the  reversal  of  the  law  of  proba- 
bilities leads  conclusively  to  the  same  solution  of  this 
question. 

If  the  probability  of  similar  averages  is  based  upon  the 
causality  of  like  circumstances  and  relations,  the  conclu- 
sion is  unavoidable  that  the  uniform  or  uniformly  changing 
figures  of  moral  statistics  must  necessarily  be  founded 
upon  a  basis  of  uniform  conditions  and  developments. 
One  can  say  that  the  regularity  of  voluntary  actions  is 


Theory  and  Technique  of  Statistics.  153 

explained  most  simply  by  concluding,  from  the  fact,  the 
same  factors  from  whose  existence  the  theory  of  proba- 
bility would  assume  the  fact. 

§  86.   STATISTICAL   REGULARITY. 

Discarding  all  fantastical  ideas  of  a  law  of  large 
numbers  or  of  unfreedom  of  the  will,  the  regularity  of 
phenomena  is  none  the  less  a  most  important  subject 
of  statistical  theory.  "  Rule  "  is  our  expression  for  the 
uniformity  and  arrangement  of  a  number  of  analogous 
phenomena.  Conformity  to  the  rule  is  regularity.  Hence 
we  may  properly  call  regularity  things  based  upon  ana- 
lytical rules  calculated  mathematically,  or  uniformities  fol- 
lowing with  necessity  from  natural  typical  premises  {e.  g.y 
that  there  are  twice  as  many  hands  as  men,  or  married 
persons  as  marriages).  In  the  same  way  the  necessary 
effect  of  a  certain  cause,  or  the  same  measure  of  effect 
with  the  same  measure  of  cause;  also  the  example  of 
Sigwart  (§  58),  when  an  object  is  found  in  relatively  equal 
portions  in  the  smaller  sections  of  a  State  as  in  the  whole, 
constitute  regularity. 

These  are  not  statistical  regularities.  Statistics  does 
not  investigate  uniformities  that  are  calculable  because 
necessary,  nor  such  as  are  typical  or  accidental.  These 
are  either  known  or  else  occur  so  that  no  more  interest 
attaches  to  their  uniformity  than  to  their  difference,  as 
long  as  no  conclusion  is  permitted  that  a  similar  number 
will  be  found  in  the  next  aggregate  not  yet  observed. 

Statistics  seeks  regularities  with  the  same  end  in  view  as 
in  enumeration,  i.  e.,  of  gaining  knowledge  of  the  confused 
and  unclassified  aggregates  of  concrete  existence.  Regu- 
larity has  value  for  statistical  methods  only  as  expectation. 
Expectation  depends,  like  all  probability,  upon  the  knowl- 
edge of  causal  connections.  This  knowledge  may  be  based 
upon  proof  or  it  may  be  assumed,  possibly  erroneously, 
but  must  always  be  conscious.     Sigwart's  example  (§58) 


154  Annals  of  the  American  Academy. 

is  applicable  statistically  only  where  there  is  an  object  in 
view. 

Conclusions  as  to  regularities  in  statistics  are  conclu- 
sions as  to  probabilities,  and  are  in  a  way  an  extension  of 
the  principle.  Probabilities  generally  attempt  to  discover 
from  the  results  of  enumeration  of  analogous  aggregates  a 
number  which  in  a  special  case  has  not  been  found  by 
enumeration.  Statistical  rules,  on  the  contrary,  look  for 
the  numerical  ratios  for  certain  phenomena  which  may 
be  expected  for  all  aggregates,  including  those  analogies 
which  have  not  been  observed.  This  inquiry  cannot  be 
conducted  in  any  other  way  than  by  determining  through 
enumeration  the  ratios  of  numerous  analogous  aggregates, 
and  taking  an  average  which  may  serve  as  a  rule. 

The  application  in  a  single  case  is  now  much  simpler.  If 
the  rule  is  once  ascertained,  it  is  no  longer  necessary  to 
compare  the  figures  for  all  the  analogous  aggregates,  but 
simply  to  examine  whether  the  aggregate  is  actually  anal- 
ogous to  those  for  which  the  rule  is  already  ascertained. 

This  reversal  of  the  procedure  facilitates  so  much  all 
statistical  efforts,  that  it  is  one  of  the  chief  aims  to  find 
such  rules.  If  rules  are  established  for  special  causes  and 
special  peculiarities  of  the  aggregate,  the  scope  of  the  rule 
is  thereby  limited.  In  applying  it  one  must  carefully  in- 
quire whether  all  these  pecularities  and  special  causes  are 
present  in  the  aggregate.  Such  special  regularities  may 
be  most  frequently  found  in  dealing  with  the  same  aggre- 
gate, but  at  different  periods.  In  such  a  case  the  non- 
applicability  of  the  rule  would  not  be  without  value,  as  it 
would  point  to  variations  of  certain  causes0  But  the  more 
special  the  causes  upon  which  the  rule  is  based,  the  more 
they  are  apt  to  be  variable  and  the  more  limited  is  the 
sphere  of  analogies.  Hence  the  more  difficult  it  becomes 
to  find  a  sufficient  number  of  analogies  from  which  to  gain 
the  rule  itself. 

The  rules  are  taken,  therefore,  largely  from  such  rela- 
tions as  appear  to  be  the  result  of  the  combined  influence 


Theory  and  Technique  of  Statistics.  155 

of  manifold  causes  known  only  in  a  general  way,  such  as 
the  influence  of  human  society  generally  or  certain  condi- 
tions of  existence  or  of  occupation,  of  rural  and  city  life, 
etc.  It  is  chiefly  in  the  field  of  the  statistics  of  popula- 
tion that  such  rules  have  been  gained.  In  particular  might 
be  mentioned  the  group  of  voluntary  actions  and  moral 
statistics,  and  also  births,  still-births,  plural  births,  mar- 
riages, deaths,  age  classes,  expectation  of  life,  sickness, 
physical  strength,  causes  of  death,  civil  condition,  occu- 
pations, and  other  conditions  of  human  life  in  which  simi- 
larity of  the  phenomena  are  observed,  as  in  the  voluntary 
actions,  and  which  furnish  proofs  of  the  influence  of  com- 
mon circumstances  leading  to  like  results. 

When  the  rules  are  of  such  a  general  character  it  is 
much  easier  to  apply  them  to  the  analogies.  They  have  a 
double  use.  In  each  new  problem  they  seem  a  probable 
solution,  and  when,  on  the  other  hand,  these  conjectures 
can  be  compared  with  the  results  of  actual  enumeration 
in  a  given  case,  they  lead  one  to  inquire  the  special  causes 
of  the  deviations. 


C.  THE   FORM   OF   THE   PROCESS. 
§  87.   THE  STEPS   IN   THE   STATISTICAL   INVESTIGATION. 

The  minute  consideration  of  the  steps  in  the  methodical 
statistical  process  has  shown  its  strictly  logical  character, 
and  the  symmetry  of  its  principles. 

The  leading  thoughts  expressed  in  §  62  are  the  basis  of 
the  special  phases  of  the  mode  of  investigation  seen  in 
§§63-86. 

These  rules  are  developed  from  a  critical  examination 
of  the  value  of  our  experience.  We  may  endeavor  to 
form  a  conception  of  a  concrete  aggregate;  we  may 
attempt  to  compare  it  with  what  we  have  observed,  or 
with  the  more  or  less  vivid  descriptions  of  others,  but  in 


156  Annals  of  the  American  Academy. 

the  final  result  we  have  only  a  conception  of  it  as  a  col- 
lective idea.  In  it  float  various  elements  that  we  cannot 
perceive.  We  may  notice  details ;  yet,  however  important 
they  may  appear  to  us,  according  to  the  subjective  bent 
of  our  minds,  they  remain  unrelated  to  the  aggregate  and 
purely  accidental. 

This  defect  of  our  faculty  of  observation  can  only  be 
overcome  by  organized  effort.  This  is  to  be  found  in  enu- 
meration, essentially  the  most  general  form  of  measure- 
ment. With  a  definite  unit  of  enumeration  the  entire  field 
of  possibility  is  measured  and  the  actual  phenomena  ascer- 
tained. The  idea  of  gaining  by  systematic  enumeration 
some  knowledge  of  the  confused  and  changing  elements 
of  an  aggregate  gives  a  fixed  and  definite  course  to  the 
entire  process.  A  deviation  from  the  course  involves  an 
error. 

The  enumeration  has  for  its  objects  certain  concrete 
things  already  defined.  One  or  more  units  may  be 
counted,  and,  indeed,  distinct  measures  for  the  various 
units  may  be  adopted.  This  will  furnish  a  somewhat 
richer  and  more  detailed  result,  but  does  not  manifestly 
affect  the  mode  of  investigation.  The  enumeration  must 
not  take  place  within  ill-defined  limits  of  time  and  space. 
The  aggregate  examined  must  have  the  appearance  of  a 
compact  definite  concrete  object.  The  results  of  the  enu- 
meration are  simply  the  totals  of  the  things  counted. 
These  give  some  description,  yet  not  such  a  one  as  would 
enable  us  to  say  that  the  totals  were  large  or  small.  Such 
a  judgment  is  the  important  thing  attaching  to  the  number 
gained.  Other  judgments  could  only  be  analytical  ones 
derived  from  the  ideas  underlying  the  problem,  and  could 
furnish  no  contribution  to  our  knowledge. 

To  reach  a  judgment  we  must  compare  number  with 
number,  totals  of  like  things  found  in  analogous  ag- 
gregates ;  i.  e.y  such  as  have  the  same  character  for  the 
purpose  of  the  inquiry.  It  is  not  contended  that  this  simi- 
larity exists  concretely  either  for  the  units  or  aggregates. 


Theory  and  Technique  of  Statistics.  157 

Similarity  exists  only  in  the  conception,  in  the  character- 
istics necessary  to  it.  All  other  characteristics  of  aggre- 
gate and  unit  can  and  must  be  very  different.  The 
comparison  teaches  how  many  things  of  the  same  kind 
are  to  be  found  in  a  series  of  aggregates  of  the  same 
kind. 

The  next  result  is  the  idea  of  variability,  or  the  limits 
and  relations  of  the  fluctuations.  Theoretically  it  would 
be  erroneous  to  attach  the  variability  to  one  aggregate. 
One  is  easily  induced  to  this  by  the  impression  that  an 
aggregate  observed  at  different  periods  is  really  the  same 
with  slight  changes  of  certain  qualities.  According  to 
§  65  a  thing  to  be  counted  cannot  be  the  same  when  an 
essential  character  changes.  And  so  an  aggregate  is  not 
the  same  in  which  the  number  of  units  to  be  counted 
changes  or  may  have  changed.  It  requires  two  enumera- 
tions to  find  out  a  change,  and  for  each  enumeration  the 
aggregate  is  different.  The  analogy  may  be  closer  when 
it  relates  to  aggregates  of  different  periods  of  time  than  to 
those  locally  distinct,  yet  theoretically  they  are  as  different 
in  the  one  case  as  in  the  other.  The  idea  of  the  aggregate 
itself,  a  confused  and  changeable  complex,  inaccessible  in 
its  inner  details  to  inductive  and  deductive  processes,  is 
contradictory  to  the  notion  that  it  might  be  considered 
as  unchanged  in  the  period  between  two  enumerations. 
All  variability  which  is  observed  statistically  relates  not  to 
one  and  the  same  aggregate,  but  to  analogous  aggregates, 
those  of  the  same  kind.  It  is  simply  the  different  fre- 
quency of  the  things  whose  proportions  describe  the 
aggregate  more  explicitly. 

Tracing  further  the  statistical  process,  we  find  for  all 
aggregates  similar  phases  in  forming  judgments.  The 
sums,  when  reduced  to  common  terms,  i.  e.,  the  possible 
differences  in  the  occurrences  of  the  phenomena,  furnish  a 
measure  for  the  quantitative  judgment  of  the  results.  This 
judgment  is  limited  to  the  aggregates  compared.  They 
cannot  furnish  a  general  standard.     It  is  a  standard,  how- 


158  Annals  of  the  American  Academy. 

ever,  suitable  for  the  purposes  of  the  problems,  inasmuch 
as  the  aggregates  compared  are  sufficiently  well  known 
indirectly  in  their  general  character. 

On  this  quantitative  judgment  we  can  solve  the 
problem  of  causal  connections  upon  the  principle  that  the 
greater  the  quantity  of  things  acting  as  causes  the  greater 
positively  or  negatively  the  number  of  things  to  be  re- 
garded as  effects. 

Like  effects  follow  from  like  causes,  and  from  the  knowl- 
edge of  causal  connections  it  is  but  a  step  to  the  conclu- 
sion that  the  average  relation  between  the  quantities  of 
cause  and  effect  in  analogous  aggregates  is  to  be  looked 
upon  as  most  probable  in  the  aggregate  under  investiga- 
tion, and  further  that  from  the  quantity  of  cause  one  may 
calculate  the  quantity  of  effect  and  vice  versa.  This  con- 
clusion is  so  strengthened  by  numerous  instances  which 
confirm  it,  that  regularity  becomes  one  of  the  premises  of 
statistical  argument. 

§  88.  predominance  of  statistical  material. 

The  sketch  of  statistical  processes  given  in  the  fore- 
going section  seems  to  have  but  little  connection  with 
ordinary  statistical  work.  Most  statistical  investigations 
show  only  portions  of  it. 

This  is  accounted  for  in  the  purpose  of  the  most  com- 
mon phase  of  statistical  work.  Nearly  all  statistical  bureaus 
are  engaged  in  preparing  matter  for  work  on  problems  of 
the  future.  This  is  true  of  official  bureaus,  of  corporations, 
and  scientific  institutions,  perhaps  in  a  still  higher  degree 
of  private  undertakings. 

It  is  in  the  nature  of  statistics  that  for  special  problems 
and  sharp  distinctions  the  analogy  between  the  aggregates 
must  be  drawn  very  close.  Hence  for  detailed  investiga- 
tions aggregates  differing  only  in  time  are  preferable  to 
those  differing  in  space.  It  is  manifest  that  an  aggregate 
remains  essentially  the  same  at  different  periods,  however 


Theory  and  Technique  of  Statistics.  159 

it  may  vary  in  its  parts.  The  fixed  elements  remain  the 
same,  and  hence  it  is  peculiarly  adapted  for  tracing  causal 
connections  by  statistical  methods. 

Questions  which  arise  from  the  practical  necessities  of 
administration  are  apt  to  be  such  as  cannot  be  solved  at 
once  by  observations  and  enumerations.  They  often  deal 
with  the  changes  which  have  taken  place  in  the  field  of 
the  administration,  and  can  only  be  answered  by  compar- 
ing past  and  present  conditions.  The  investigation  requires 
constant  or  periodical  observations  in  order  to  determine 
numerically  the  changes  which  have  occurred.  In  all 
statistical  bureaus  a  system  of  providing  for  future  uses 
has  been  developed,  which  far  exceeds  in  extent  actual 
solutions,  and  forms  the  main  contents  of  the  publications 
described  in  §§  50  and  75.  At  each  point  there  are  certain 
data  which  it  is  considered  necessary  to  collect  continu- 
ously or  periodically.  In  no  case  do  they  approach  in 
comprehensiveness  the  field  which  the  Statistical  Congress 
regarded  proper  for  such  statistics.     (Appendix  II.) 

The  necessary  restrictions  of  the  field  have  already  been 
noticed  (§  50).  The  great  bulk  of  statistical  publications 
belongs  to  the  class  of  preparatory  statistics. 

It  is  profitable  to  establish  rules  as  to  what  material  is 
the  most  desirable  under  given  conditions.  Such  rules 
might  be  called  rational  statistics.  But  statistical  practice, 
with  its  changing  needs,  is  rarely  dependent  to  any  great 
degree  upon  such  a  theory.  Not  only  in  different  coun- 
tries, but  also  in  the  same  State,  objects  of  enumeration 
and  the  treatment  of  them  are  only  too  often  changed 
according  to  circumstances. 

But  whatever  view  may  be  held  in  the  matter,  it  cannot 
be  doubted  that  this  phase  of  statistical  activity  brings 
about  a  peculiar  conception  and  treatment  of  the  material. 
This  must  be  examined,  and  its  relation  to  the  method  of 
solving  statistical  problems  explained. 


160  Annals  of  the  American  Academy. 

§  89.  the  elaboration  of  systematic  statistics. 

I  The  comprehensive  labors  of  statistical  bureaus  which 
J  /collect  data  in  all  fields  of  statistics  for  future  use  may 
well  be  termed  systematic  statistics.  Such  statistics  col- 
lect material  for  the  problems  which  experience  tells  us 
are  the  most  frequent  and  important  in  the  history  of 
States.  In  following  these  facts  regularly  the  material 
(§§  1  and  60)  itself  becomes  of  interest.  The  observation 
and  discussion  of  a  single  object  is  not  based  entirely  on 
the  problem  to  be  solved,  but  each  object  is  examined  to 
find  the  best  possible  and  most  fruitful  investigations  which 
might  be  undertaken  in  connection  with  it.  It  is  necessary 
to  study  carefully  the  phenomena,  to  examine  its  causes 
and  effects  and  their  connection,  and  thus  form  a  judgment 
as  to  the  nature  and  practicability  of  the  observations  which 
seem  to  promise  the  most  information. 

Thus  theories  spring  up  as  to  how  certain  branches  of 
statistics,  as  of  population,  industries,  transportation,  and 
the  like,  may  be  most  effectively  treated.  These  are  ques- 
tions of  methods,  but  lead  also  to  investigations  of  the 
nature  of  the  conditions  and  changes  of  population,  popu- 
lar wealth  and  popular  morals,  public  economy  and  na- 
tional strength.  This  is  the  reason  that  a  large  number 
I  of  influential  statisticians  hold  that  statistics  is  essentially 
^  the  science  of  human  societies  (§  56).  In  opposition  to 
this  view  one  may  justly  object  that  a  systematic  knowl- 
edge of  human  society  which  did  not  at  the  same  time 
include  the  historical,  geograghical,  anthropological,  physi- 
ological, and,  finally,  also  the  philosophic  consideration  of 
it  could  not  be,  after  all,  a  science.  It  can,  none  the  less, 
be  an  important  subject  for  instruction.  This  school  of 
statisticians  has  produced,  however,  the  practically  and 
theoretically  important  branches  of  knowledge  which  we 
designate  statistics  of  population,  medicine,  finance,  eco- 
nomics, morals,  and  so  forth.  At  the  same  time  we  should 
remember  that  we   already   possess   a   certain   body   of 


Theory  and  Technique  of  Statistics.  161 

facts  for  each  of  these  subjects.  We  know  certain  regu- 
larities, probabilities,  causes  and  quantitative  relations,  and 
principles  of  determining  these  relations. 

If  it  should  be  asked  how  this  conception  and  treatment 
of  the  material  affect  the  features  of  the  method  described, 
it  cannot  be  overlooked  that,  however  exact  and  careful 
these  statisticians  have  been,  the  methods  of  statistics 
require  the  same  care  and  exactness  for  all  problems. 

THE   TENDENCIES   OF   SYSTEMATIC   STATISTICS. 

Systematic  statistics  has  given  to  statistical  processes 
some  peculiar  features.    Two  things  could  not  fail  to  affect 
the  contents  and  mode  of  treatment.     First,  the  observa^  i  \ 
tions  are  confined  to  one  country  and  to  essentially  the 
same  group  of  objects.     Secondly,  they  are  governed  not 
by  the  special  needs  of  a  particular  problem,  but  by  general .% 
considerations  which  take  up  the  problems  in  a  general \~- 
way,  collecting  materials  for  their  solution,  but  not  at- 
tempting a  solution. 

Confining  the  observations  to  one  State,  and  making 
them  continuous  or  periodical,  render  almost  wholly  super- 
fluous one  of  the  fundamental  requirements,  the  determi- 
nation of  the  aggregate  and  its  limits  in  time  and  space. 
These  are,  then,  matters  of  course.  On  the  contrary,  the 
possibility  of  future  use  gives  the  highest  importance  to 
the  distinctions  between  the  smaller  subdivisions  of  the 
State.  Even  when  the  problem  might  be  solved  by  the 
totals  of  the  entire  State  a  great  number  of  subdivisions  is 
deemed  advisable.  A  large  number  of  subdivisions  are 
made  for  the  enumerators,  and  while  it  is  not  meant  that 
all  these  are  distinguished  in  the  results,  it  is  true  of  the 
most  important  of  them,  counties,  townships,  etc. 
1  Not  only  the  aggregates,  but  also  the  units,  are  deter- y 
mined  by  general  considerations  instead  of  special  needs. 
The  group  of  enumerated  units  is  extended  in  view  of  their 
probable  causal  connection  as  far  as  possible  without  over- 


1 62  Annals  of  the  American  Academy. 

burdening  the  enumeration.  The  choice  is  made  so  as 
to  avoid  counting  the  units  of  a  general  nature,  and 
also  others  which  are  merely  subdivisions  of  them.  The 
subdivisions  are  counted  so  that  the  sums  will  give  the 
total.  In  this  manner  a  more  correct  enumeration  of  the 
qualified  units  is  secured,  and  at  the  same  time  the  totals 
for  a  larger  group  of  units  obtained.  These  may  possibly 
be  important.  Absolute  uniformity  of  the  enumeration  in 
the  time,  determination  of  ideas  and  organization  increases 
its  value  for  comparison.  There  is  frequently  combined 
with  the  systematic  preparation  of  the  data  the  calculation 
of  ratios  for  some  of  the  more  usual  comparisons. 

The  entire  system  excels  in  clear  distinctions  between 
aggregate,  unit,  and  ratio,  and  a  plan  of  arrangement  which 
furnishes  easily  understood  results.  This  is  also  reflected 
in  the  presentation  of  the  results.  The  fruit  of  all  these 
labors  are  the  great  compilations  of  tables,  in  which  the 
data  are  arranged  with  the  greatest  detail  possible,  but  in 
which  conclusions  and  definite  problems  are  only  excep- 
tionally included.  This  form  does  not,  however,  warrant 
any  conclusion  that  there  is  any  difference  in  principles. 
All  the  results,  as  far  as  no  special  questions  are  to  be 
solved,  are  to  be  classed  as  statistical  material  (§§  73  and 
/    78).     It  is  not  the  final  purpose  of  the  investigations. 

§91.    THE   PROBLEMS  OF  SYSTEMATIC   STATISTICS. 

Systematic  statistics  has  been  highly  developed,  and 
presents  certain  phases  of  statistical  processes  in  a  very 
favorable  light.  But  it  cannot  be  denied  that  it  has 
done  little  to  promote  a  correct  conception  of  the  real 
purpose  of  the  process,  and  hence  of  the  real  character  of- 
statistics  generally.  Its  influence  may  be  characterized, 
theoretically  as  tending  to  show  that  the  investigation  of 
I  \  the  units,  and  not  of  the  masses,  was  the  object  of  statis- 
tical inquiry.  This  misconception  permits  of  ready  expla*- 
nation.     The  aggregates  have  become  fixed  and  appear  to 


ll 


Theory  and  Technique  of  Statistics.  163 

be  always  the  same.  The  group  of  things  observed  is  apt 
to  be  always  the  same.  It  comprises  the  persons  and 
things  which  have  the  greatest  value  for  the  people  and 
the  nation,  and  which,  when  investigated,  give  the  best 
characterization  of  the  latter.  These  persons  and  things 
are  in  their  essential  qualities  typical,  and  are  so  treated  in 
every  statistical  observation.  All  that  is  asked  is,  Do  they 
exist?  and  if  so,  have  they  certain  qualities?  In  the  same 
manner  they  are  observed  in  the  changes  of  their  mutual 
relations.  And  as  the  result  of  all  observations  there 
appears  to  be  no  other  result  than  a  certificate  of  these 
changes. 

Hence  it  is  not  strange  that  attention  should  not  be 
given  to  the  aggregate,  which  is  regarded  as  a  matter  of 
course,  but  that  it  should  centre  in  the  objects.  It  may 
appear  to  be  more  important  and  more  useful  to  base 
any  further  investigation  immediately  on  the  persons  and 
things.  One  may  discover  a  gain  for  statistical  processes 
in  permitting  an  investigation  of  typical  things  with  refer- 
ence to  their  variable  elements. 

Unfortunately  this  apparently  simple  and  attractive  con- 
ception, however  widely  held,  is  inadmissible.  For  the 
correctness  of  statistical  conclusions,  as  well  as  the  appli- 
cation of  results,  it  is  confusing  and  in  most  cases  danger- 
ous. It  forms  a  generalization  for  which  absolutely  no 
foundation  is  to  be  found  in  statistics  and  for  which  statistics 
cannot  be  responsible. 

No  statistical  judgment  deals  with  the  unit,  but  strictly 
and  only  with  the  aggregate.  The  variable  elements  of 
persons  and  things  otherwise  typical,  that  are  enumerated, 
are  always  counted  in  a  specific  aggregate  and  under  cer- 
tain specific  circumstances.  The  qualities  of  the  objects 
themselves,  so  far  as  they  are  not  typical,  or  the  subject 
of  the  investigation,  are  completely  unknown.  There  is 
absolutely  no  presumption  that  these  other  qualities  are 
typical  or  permanent  in  the  aggregate  observed,  and  much 
less  beyond  its  limits. 


164  Annals  of  the  American  Academy. 

When  the  person  or  thing  has  no  relation  to  an  aggre- 
gate it  is  wholly  immaterial  whether  the  variable  elements 
are  observed  statistically  or  in  individual  cases.  A  gene- 
ralization from  them  is  inductive.  If  the  quality  is  typical, 
statistical  inquiry  is  unnecessary;  if  it  is  not  typical,  then 
it  is  only  known  where  it  is  observed,  or  where  a  conclu- 
sion upon  observations  leads  us  to  expect  it  upon  the  basis 
of  probabilities.  Even  such  a  general  rule  that  for  20 
girls  21  boys  are  born,  does  not  hold  except  within  the 
range  of  the  analogy,  that  is,  within  civilized  States. 
Whether  or  not  this  condition  exists  in  China  nobody 
knows,  and  anybody  who  claims  that  it  does  places  him- 
self upon  an  anthropological  induction,  not  upon  a  statis- 
tical probability. 

§92.  the  form  of  the  question  in  systematic 
statistics. 

Systematic  statistics  must  have  as  a  basis  a  definite 
aggregate  in  solving  any  problem,  and  its  excellent  and 
elaborate  material  occupies  exactly  the  same  position  as 
any  other.  This  may  be  shown  again  by  an  examination 
of  the  form  of  the  question,  which  is  the  kernel  of  every 
problem. 

The  form  of  the  question  is,  in  the  operations  of  system- 
atic statistics,  as  a  rule,  peculiar.  The  questions  raised  in 
the  preliminary  observations  to  the  compilations  of  tables, 
are  not  devoted,  as  a  rule,  to  single  aggregates.  On  the 
contrary,  they  discuss  the  aggregates  having  the  phenom- 
ena in  the  greatest  and  least  intensity  and  the  relations 
between  them  in  this  respect. 

It  would  seem  that  with  this  peculiar  manner  of  dis- 
cussing the  material  there  must  be  some  change  in  the 
nature  of  the  problems  arising  from  it.  But  closer  con- 
sideration reveals  the  fact  that  the  general  theoretical 
scheme  has  not  been  departed  from. 

One  question  appears  at  a  certain  phase  of  every  sta- 


1( 


Theory  and  Technique  of  Statistics.  165 

tistical  problem.  It  occurs  first  in  the  comparison  of 
analogies.  It  is  the  question  discussed  in  §87,  of  the  J  I 
variability  of  phenomena ;  i.  e.y  the  question  of  the  rela- 
tions of  the  fluctuations.  Upon  this  is  based  the  deter- 
mination of  the  average,  the  consideration  of  the  minima 
and  maxima,  and  the  entire  conception  of  the  progression 
of  the  series.  This  shows  that  the  discussion,  when  ap- 
plied to  the  various  aggregates,  is  only  another  form  of 
treating  the  same  subject. 

Any  attempt  to  answer  questions  upon  the  basis  of  this 
combination  will  show  that  it  admits  of  no  use  for  any 
purposes  not  derived  from  the  analogy  of  the  aggregates 
in  question.  Thus,  in  the  example  of  §  75,  the  question 
is  permissible,  which  district  has  had  the  greatest  growth 
of  population,  or  whether  it  has  been  greatest  for  the  dis- 
trict A.  But  if  the  question  is  whether  all  the  districts 
or  the  district  A  have  had  a  large  growth  of  population, 
these  data  are  worthless,  because  the  question  calls  for  a 
different  analogy.  In  this  case  each  district  separately  or 
the  entire  number  must  be  compared  with  these  conditions 
at  an  earlier  period. 

But  if  we  leave  the  field  of  quantitative  judgments, 
w^iere  there  is  a  greater  measure  of  freedom,  and  proceed 
to  the  judgment  of  causalities,  it  is  evident  that  for  the 
indication  of  causes  we  cannot  proceed  from  a  plurality  of 
aggregates,  but  only  from  the  single  aggregate,  unless, 
indeed,  the  plurality  is  regarded  as  a  whole.  The  ques- 
tion why  in  district  A  the  growth  of  population  has  been 
greatest  separates  immediately  the  different  districts.  It 
must,  therefore,  follow  that  unless  the  results  obtained  are 
to  be  useful  simply  in  accidental  cases,  they  must  form 
part  of  some  previously  arranged  problem.  It  is  charac- 
teristic of  systematic  statistics  that  it  takes  such  problems 
into  consideration.  To  argue  correctly  and  avoid  all 
errors  we  must  go  back  to  the  starting-point  required  by 
the  method ;  in  other  words,  we  must  start  from  a  single }  \ 
aggregate,  or  what  is  the  same  thing,  a  total  of  them. 


1 66  Annals  of  the  American  Academy. 

§  93.  form  of  judgments  of  causality  and 
probabilities. 

The  form  which  the  judgment  of  causality  and  proba- 
bility is  apt  to  assume,  has  also  a  tendency  to  prevent  the 
proper  conception  of  the  methodical  process.  It  follows 
from  the  fact  that  the  labor  of  collecting  the  data  and 
preparing  the  returns  for  publication  is  out  of  all  propor- 
tion to  that  required  to  formulate  the  conclusions  arising 
out  of  them.     Yet  these  are  the  final  results. 

As  a  rule  it  is  quite  sufficient  to  prepare  the  material  up 
to  the  quantitative  comparison.  This  enables  a  specialist 
to  form  his  conclusion  in  a  short  time.  Hence  a  very 
large  portion  of  the  material  is  collected,  and  presented  to 
the  public  in  compilations,  without  any  attempt  at  drawing 
conclusions.  It  does  not  seem  advisable  to  do  so  until 
some  necessity  for  it  arises.  When  it  is  necessary  to 
form  a  judgment  one  can  seldom  wait  until  some  new 
special  material  for  it  has  been  gathered.  By  far  the 
greater  number  of  problems  which  arise  must  be  answered 
from  existing  material. 

The  publications  of  official  statistics  have  therefore  the 
character  of  store-houses  of  information.  The  same  *Adty 
be  said  of  private  statistics  which  offer  informati''  a  for 
general  use.  Such  are :  Gothaische  Genealogische  Kalen- 
dar  (§  18);  G.  Fr.  Kolb,  Handbuch  der  Vergleichende 
Statistik,  1857;  Brachelli,  Staaten  Europas,  1853;  Martin, 
Statesman's  Year-book,  1864;  Brachelli,  Statististische 
Skizze,  1868;  Legoyt,  La  France  et  l'Etranger,  1864; 
Michael  G.  Mulhall,  The  Progress  of  the  World,  1880,  and 
the  Dictionary  of  Statistics,  London,  1884. 

When  official  statisticians  discuss  the  conclusions  to  be 
drawn  from  data,  they  are  apt  to  do  so  in  periodicals  and 
in  historical  or  political  works.  In  the  bureaus  themselves 
the  discussion  of  such  matters  is  limited  to  the  needs  of 
the  organization. 

Nevertheless,  there  are   statistical   problems  requiring 


Theory  and  Technique  of  Statistics.  167 

very  extended  and  complicated  calculations  and  estimates 
for  the  conclusions  to  be  drawn  from  them.  But  this  does 
not  place  them  outside  of  the  usual  processes.  In  this  num- 
ber should  be  classed,  for  instance,  statistics  of  trade  in 
commodities.  The  aggregate  to  be  considered  is  the  cus- 
toms limits,  and  totals  have  no  other  divisions  than  those 
of  time,  where  months  or  quarters  may  be  distinguished. 
The  units  are  the  different  articles,  which  are  further 
distinguished  as  goods  exported,  imported,  in  transit, 
warehoused,  etc.  The  material  is  counted  by  pieces  and 
weight,  the  results  examined  and  grouped.  From  this  we 
can  compare  the  different  units  in  time  and  compare  their 
quantity.  A  simple  change  in  quantity  does  not  show 
certain  essential  matters  sufficiently,  unless  there  is  some 
grouping  by  degrees  of  quality,  and  the  value  of  the  total 
of  each  group  determined. 

This  necessitates  appraisement  by  experts,  and  for  this 
purpose  a  comprehensive  knowledge  of  prices  is  requisite 
with  all  the  difficulties  in  its  application  which  are  pointed 
out  in  §65.  The  statistics  of  trade  are,  therefore,  worked 
over  in  a  double  way,  and  are  one  of  the  most  important 
tasks  of  statistics  (Gesetz  iiber  die  Statistik  des  Waaren- 
verkehrs  des  deutschen  Zollgebiets  mit  dem  Auslande, 
v.  20,  6.  1879;  nebst  Ausfuhrungsbest.,  2  A.  1885  ;  R.  G. 
B.,  S.  261 ;  Central  Bl.,  p.  676;  Stat.  d.  D.  R.,  Bd.  43). 

Another  example,  very  different,  yet  very  complicated, 
is  to  be  found  in  mortality  tables.  The  simplest  rudimen- 
tary forms  have  been  discussed  (§  14).  More  exact  forms 
give  rise  to  intricate  and  delicate  problems  (Appendix 
VII.).  The  simplest,  as  well  as  the  most  complicated,  is  a 
judgment  of  probabilities.  The  combination  of  the  year 
of  birth  or  the  age  of  the  dying  with  the  living  persons 
of  a  given  population,  furnishes  the  probability  of  death. 
If  one  goes  a  step  further,  and  from  a  single  death  table  or 
a  comparison  of  several  arrives  at  the  order  of  death  of  a 
large  group  of  populations,  we  find  a  statistical  regularity. 
It  is  not  necessary  to  discuss  the  similar  problems,  only 


1 68  Annals  of  the  American  Academy. 

slightly  less  complicated,  which  might  be  drawn  from  the 
statistics  of  agriculture,  of  finance,  of  trade,  or  of  medicine. 
The  requirements  of  the  technique  show  also  the  definite 
internal  workings  of  the  method. 


V 


D.  THE  REQUIREMENTS   QF  THE  TECHNIQUE. 
I.  The  Problem  and  the  Plan. 

§94.    THE  SEPARATE   PHASES   OF  THE  TECHNICAL  PROCESS. 

There  are  certain  distinct  processes  which  are  to  be 
observed  in  the  solution  of  every  problem  of  empirical 
investigation,  and  upon  closer  analysis  even  in  all  our 
synthetical  judgments.  They  proceed  from  the  develop- 
ment of  the  idea,  to  procuring  the  means  of  proof,  to  the 
examination  of  the  latter,  to  the  answering  of  objections, 
and  finally  to  incorporating  the  result  in  our  general 
knowledge.  In  statistical  problems  these  phases  appear 
with  unusual  distinctness. 
*/  No  matter  what  the  statistical  problem  may  be,  it  must 
proceed  according  to  a  frfjm*  It  is  always  a  specific  ques- 
tion which  may  be  answered  in  several  more  or  less  ac- 
curate ways.  The  end  in  view  and  the  resources  which 
can  be  drawn  upon  will  indicate  in  which  manner  and 
within  which  limits  the  answer  is  to  be  given.  According 
to  the  choice  made,  it  may  be  very  simple  or  very  com- 
plicated. But  under  all  circumstances  a  definite  plan  pro- 
viding for  all  the  details  is  an  absolute  prerequisite.  The 
means  of  proof  are  collected  according  to  this  plan.  They 
may  be  gathered  from  material  in  existence  or  by  special 
observations  and  enumerations  of  greater  or  less  compli- 
cation and  extent.  The  means  of  proof  must  be  subjected 
to  a  critical  examination,  they  must  be  sifted,  errors  cor- 
rected, and  compared  with  known  facts.     By  this  prepara- 


Theory  and  Technique  of  Statistics.  169 

tion  they  are  ready  for  use.  The  question  must  now  be 
answered  and  presented  in  its  details,  so  that  it  is  summar- 
ized, and  yet  sufficiently  clear  to  enable  an  expert  to 
examine  the  premises.  Finally,  provision  must  be  made 
that  the  knowledge  gained  shall  not  be  lost.  It  is  neces- 
sary to  preserve  not  only  the  conclusion,  but,  as  far  as 
possible,  all  that  leads  up  to  it,  for  future  reference.  It  is 
probable  that  it  will  be  needed  to  solve  future  problems. 

§95.    DEVELOPMENT   OF   THE   PLAN. 

A  statistical  problem  grows  out  of  a  practical  or  scientific  \\ 
need.  It  is  always  a  clear  and  distinct  question  as  to  some 
concrete  relations.  The  answer  to  the  question  is  always 
the  number  of  times  in  which  certain  objects  occur  in  a 
confused  and  changing  aggregate,  and,  further,  the  rela- 
tions of  a  quantitative,  causal,  or  probable  nature  which 
such  objects  bear  to  one  another.  The  answer  can  only 
be  obtained  by  comparing  the  number  of  objects  in  aggre- 
gates of  a  like  nature. 

The  range  which  remains  open  for  the  mode  of  answer 
is,  as  a  glance  at  the  method  shows,  very  broad.  The 
aggregate  and  the  purpose  of  the  problem  are  the  only 
fixed  elements.  Within  certain  limits  the  choice  of  ob- 
jects to  be  counted  is  free.  Theory  shows  that  one  unit 
may  sometimes  be  used  in  place  of  another  (§81).  This 
is  especially  true  when  it  is  wished  to  judge  of  abstract 
peculiarities  or  qualities  of  the  aggregate  rather  than  actual 
phenomena.  In  this  case  the  objects  counted  act  only  as 
indications,  which  are  to  be  chosen  with  reference  to  the 
reliance  which  can  be  placed  upon  them.  And,  further, 
the  characteristics  of  the  object  chosen  may  be  clearly 
distinguished  and  sharply  drawn,  or,  on  the  contrary, 
may  be  less  well  defined,  giving  less  exact  results.  Such 
characteristics  might  be  chosen  because  of  the  facility  of 
enumerating  them. 

The  investigation  can  choose  simple   or   complicated 


170  Annals  of  the  American  Academy. 

methods  in  ascertaining  the  number.  Instead  of  observa- 
tion and  enumeration,  easy  or  difficult  according  to  cir- 
cumstances, estimates  may  be  used.  The  use  of  estimates, 
particularly  when  they  are  based  upon  remote  probabilities, 
is  almost  unlimited.  It  depends  wholly  on  the  degree  of 
exactness  required,  or  which  can  be  considered  satisfactory 
under  the  circumstances. 

Finally,  the  choice  of  the  analogous  aggregates  to  be 
drawn  into  the  comparison  is  (§  74)  as  to  extent  wholly  at 
the  discretion  of  the  person  who  is  forming  the  judgment. 

From  all  these  considerations  it  follows  that  statistics 
is  rarely  at  a  loss  for  an  answer  to  any  question  which 
may  be  put.  Yet,  in  every  case,  with  increased  resources 
it  can  give  a  more  satisfactory,  more  comprehensive  and 
reliable  answer.  The  most  important  question  for  the 
expert  is  whether  the  material  at  hand  is  sufficient  for  the 
answer,  or  whether  new  observations  and  enumerations 
are  necessary  and  appropriate. 

New  investigations  require  for  most  statistical  problems 
an  extensive  organization  of  officials.  As  a  rule,  it  is  not 
the  statistician  who  first  proposes  the  question  and  pro- 
vides the  means  of  answering  it,  but  the  State,  corporations, 
economic  or  scientific  bodies. 

Hence  the  plan  of  investigation  depends  largely  on  the 
means  at  the  disposal  of  the  expert.  These  means  will 
depend  on  the  judgment  of  a  superior  official,  who  must 
be  convinced  of  the  amount  of  expenditure  necessary  to 
obtain  a  satisfactory  solution  of  the  problem. 

The  decision  as  to  the  mode  of  execution  will  depend 
upon  the  absolutely  necessary  requirements  of  the  problem, 
the  limit  of  time  allowed,  and  the  greatest  pecuniary  ex- 
penditure permissible.  When  this  is  determined,  it  may 
be  considered  whether  the  plan  may  be  extended  without 
interfering  with  the  purpose  or  increasing  the  cost,  so  as 
to  include  further  data  of  practical  and  scientific  impor- 
tance. In  any  case,  the  entire  plan  will  depend  largely 
from  the  clearness  with  which  the  estimates  of  the  time 


Theory  and  Technique  of  Statistics.  171 

and   cost  for   the  different   processes  can  be  made  and 
compared. 

§96.   ESTIMATES   OF  TIME  AND   COST. 

Estimating  the  time  and  cost  connected  with  statistical 
investigations  is  greatly  facilitated  by  the  fact  that  they 
consist  of  a  repetition  of  exactly  the  same  process  for  a 
large  area.  In  a  case  of  necessity  it  is  practicable  to  make 
the  enumeration  for  a  small  section  in  order  to  gain  a 
basis  of  calculation. 

The  costs  of  every  statistical  undertaking  are  distributed^ 
over  the  preparation,  the  enumeration,  and  the  examina- 
tion of  the  results.  The  preparation  includes  complete 
organization,  direction,  and  drill  of  the  enumerators,  the 
printing  and  distribution  of  the  schedules  for  their  use. 
The  enumeration  necessitates  payments  to  the  enumerators 
and  other  officials  for  their  expenses  and  their  labors.  The 
examination  brings  with  it  the  expenses  for  the  services  of 
more  or  less  expert  officials  for  the  examination  of  returns, 
corrections,  the  tabulations,  and  in  addition  the  cost  of  pub- 
lication. Schedules  and  publications  are  estimated  by  the 
amount  of  paper  and  printing,  labor  by  time,  and,  besides 
these,  packing,  expressage,  rent,  furniture,  heating,  light- 
ing, and  attendance,  all  at  current  prices. 

It  is  easily  seen,  for  an  undertaking  such  as  the  enumer- 
ation of  population,  how  many  schedules  are  necessary  for 
1000  inhabitants,  either  for  lists  or  for  cards.  The  time 
for  the  enumeration,  the  number  of  questions  asked,  the 
amount  of  cooperation  on  the  part  of  those  counted,  will 
determine  the  number  which  can  be  finished  by  an  enu- 
merator in  a  certain  number  of  hours,  and  how  much  time 
will  be  required  for  reading  for  corrections. 

The  chief  point  is  always  the  examination.  If  lists  or 
cards  have  been  collected  for  45  million  persons,  and 
there  are  12  answers  for  each  person,  it  will  be  necessary 
to  make  and  calculate  540  million  items.     It  can  by  trial 


172  Annals  of  the  American  Academy. 

be  easily  ascertained  how  many  seconds  are  necessary  for 
a  small  number  of  items,  and  for  their  addition.  Five  sec- 
onds for  each  item  would  make  2700  million  seconds,  or 
750,000  hours,  or  125,000  days  of  six  working  hours  each, 
which  finally  would  equal  the  labor  of  417  men  for  one 
year  or  139  men  for  three  years.  In  a  similar  manner 
the  most  complicated  estimates  may  be  calculated.  Every 
combination  of  questions  is  at  least  equal  to  a  further 
question.  All  necessary  reductions  must  be  calculated 
by  the  number  of  multiplications  and  divisions  necessary. 
Hence  one  can  decide  beforehand  whether  it  is  not  de- 
sirable to  omit  certain  items,  because  their  consideration 
would  involve  too  great  an  expenditure  of  time  and  labor. 

In  a  similar  fashion  we  may  form  from  the  details  an 
accurate  idea  of  the  space  which  the  printed  tables  will 
occupy.  It  is  absolutely  indispensable  to  form  from  the 
start  a  precise  idea  of  the  tables  in  which  the  chief  results 
are  to  be  grouped.  The  number  of  figures  which  will  be 
required  for  each  column  and  the  number  of  columns  are 
easily  ascertained,  and  then  the  necessary  breadth  of  the 
table.  The  number  of  lines  depends  altogether  upon  the 
number  of  subdivisions  of  the  chief  sum.  The  number  of 
lines  shows  the  length.  Suppose  the  chief  sum  Prussia 
contains  figures  of  4  to  10  places  in  50  columns,  in  all,  for 
instance,  400  figures;  and  if  this  is  to  be  divided  according 
to  the  54,000  boroughs,  there  will  be  required  a  breadth 
of  4  folio  pages,  and  1000  X  60  lines  in  length,  i.  e.t  a  work 
of  1000  sheets.  The  costs  of  composition  and  printing 
would  come  to  about  ioo,oco  marks,  and  an  edition  of 
1000  copies  would  require  2050  reams  of  paper.  In  this 
way  it  is  simple  to  calculate  by  figures  and  pages  how  far 
the  subdivisions  may  be  entered  into  when  the  funds  at 
disposal  are  limited  in  amount.  What  cannot  be  printed 
is,  as  a  rule,  worthless,  and  should  not  be  examined  or 
collected. 

(E.  Engel,  Die  Kosten  der  Volkszahlung  Zeitschr.  des 
K.  Preuss.  Statist.  Bureaus,  X.  Jahrg.  1870,  p.  42;   Preuss. 


Theory  and  Technique  of  Statistics.  173 

Statistik,  Heft  XXIX.,  2  Halfte  Vorwort,  p.  VIII. ;  Erfor- 
derniss  an  Drucksachen,  Preuss.  Statistik,  Heft  XXXIX., 
2  Halfte,  p.  50;  Kostenanschlag  der  Berufsstatistik  von 
1882,  Drucksachen  des  Deutschen  Reichtages,  5  Leglper, 
I  Sess.  1881-82,  N.  27.) 


§97.    FIRST   DRAFT   OF   THE    PLAN. 

The  decision  as  to  the  plan  to  be  pursued  in  solving  the 
problem  may  favor  the  use  of  material  already  in  exist- 
ence, supplemented  by  conclusions  based  on  probabilities. 
It  may  be  deemed  advisable  to  furnish  a  basis  for  the 
conclusions  by  ascertaining  certain  data  by  means  of  the 
enquete  or  enumeration.  All  such  methods  are  only 
means  of  facilitating  the  complete  methodical  processes 
which  rest  in  principle  upon  enumeration.  They  are  in 
part  explained  through  the  theory  and  technique  of  the 
process  of  enumeration.  In  using  them  one  can  never 
feel  secure  unless  in  a  position  to  survey  all  the  known 
data,  and  to  examine  whether  it  is  based  upon  enumera- 
tions actually  meeting  all  the  requirements  of  the  theory. 

We  must  in  theory  have  a  plan,  by  which  it  is  proposed 
to  collect  the  means  of  proof.  The  plan  when  elaborated 
must  provide  clearly  for  the  collection  of  the  material,  and 
also  for  the  proper  use  of  it  in  forming  conclusions.  For 
the  technical  execution  of  the  plan,  the  utilization  of  the 
results  is  for  the  present  of  minor  importance.  The  char- 
acter of  the  data  themselves  will  determine  their  use. 
CThe  first  technical  requirement  is  the  composition  of 
the  regulations  for  obtaining  the  actual  data,  by  enumera- 
tion or  other  methods.  The  enumeration  is  a  practical 
undertaking,  the  first  step  in  the  realization  of  the  plan. 
Once  commenced,  it  will  not  admit  of  change  or  variation 
without  endangering  completely  the  value  of  the  results. 
Hence  it  is  absolutely  essential  that  the  plan  should  in- 
clude a  carefully  worked-out  scheme  of  the  entire  process 
of  enumeration.  As  a  rule,  the  execution  of  a  plan  is  often 


174  Annals  of  the  American  Academy. 

beyond  the  influence  of  the  statistician  who  framed  it. 

From  it  the  enumerating  official  can  only  draw  a  few  very 

general  conclusions.     Hence  the  statistician  should  never 

V  [neglect  to  work  out  his  plan  into  the  last  details,  so  that 

\ihe  himself  could,  if  called  upon,  furnish  all  the  regulations 

^necessary.      Only  when  this  is  done  can  there  be  any 

*  sufficient  guaranty  of  the  practicability  of  the  plan. 

The  notion  of  the  aggregate  and  of  the  units  of  enumer- 
ation must  be  so  clearly  defined  that  absolutely  no  room 
for  misapprehension  remains,  and  every  step  of  the  pro- 
cess must  be  carefully  prepared  in  order  to  avoid  confusion. 
There  must  be  no  doubt  of  the  suitability  and  practicability 
of  the  organization.  Appropriate  provision  must  be  made 
for  the  organs  of  enumeration,  the  means  of  observation, 
and  the  manner  in  which  the  observations  are  to  be  pre- 
served and  summarized.  A  schedule  for  the  enumeration 
with  the  necessary  explanations  and  directions  must  make 

M  unmistakably  clear  what  things  are  to  be  counted,  what 
particular  characteristics,  and  what  distinctions  and  com- 
binations are  to  be  noted.  In  the  same  manner  it  must  be 
clearly  understood  exactly  what  result  is  expected.  Hence 
no  plan  can  dispense  with  a  schedule  for  the  tabulation 
showing  at  a  glance  all  the  elements  which  are  to  enter 
into  the  final  result.  It  is  only  by  comparison  of  these 
prospective  totals  with  the  questions  upon  the  collection 
schedules  that  one  can  see  how  far  the  latter  are  com- 
plete. This  comparison  does  much  to  make  clear  the 
nature  of  the  whole  operation. 

None  of  these  requirements  can  be  neglected  without 
danger  to  the  plan.  The  complete  contents  and  final 
purpose  may  indeed  remain  a  secret  of  the  expert.  But 
for  the  public  in  general  there  must  necessarily  be  definite 
regulations  for  the  business  of  enumeration. 

(Examples — Statistique  des  Deces,  1855,  Compte  rendu 
general  (§  48),  p.  42 ;  Statistique  du  Systeme  et  des  Insti; 
tutions  de  Prevoyance,  1855,  P-  I52J  Statistique  des 
Finances,  1857,  p.  245  ;   Bericht,  betr.  Ermittelungen  der 


Theory  and  Technique  of  Statistics.  175 

landwirthschaftlichen  Bodenbenutzung  und  Ernteertrage, 
1871,  Stat,  des  Deutsch.  Reichs  (§35),  Bd.  I.  p.  102; 
Bericht,  betr.  die  Statistik  der  See  SchifFfahrt,  1871,  Ibid. 
p.  229;  Plan  fur  die  Deutsche  Forststatistik,  1874,  Ibid. 
Bd.  XIV.  p.  52;  Vorbereitung  einer  Deutschen  Medizinal- 
statistik,  1874,  Ibid.  p.  I.  156;  Volks  und  Gewerbezahlung 
am  1  December,  1875,  Ibid.  Bd.  XIV.  p.  I.  24,  and  Bd. 
XX.  Th.  I.  p.  1,  51;  Preussische  Statistik,  Heft  XXXIX.,  2 
Feb.  1882;  Gesetz  iiber  die  Erhebung  einer  Deutschen 
Berufsstatistik  von  5  Juni,  1882,  Stat.  d.  Deutsch.  Reichs, 
Bd.  LIX.  p.  I.  2,  and  Neue  Folge,  Bd.  I.  p.  4;  Centralbl. 
d.  Deutsch.  Reichs,  1882,  p.  48.) 

§98.    INSTRUCTIONS   TO   ENUMERATORS. 

The  instructions  to  the  enumerators  must  indicate  clearly 
the  methods  and  scope  of  the  investigation.  It  cannot  be 
advantageous  to  have  plan  and  instructions  drawn  up  by 
different  persons.  If  the  same  person  composes  both,  one 
acts  as  a  check  upon  the  other,  and  compels  the  most  un- 
mistakable precision.  If,  on  the  other  hand,  a  second  per- 
son issues  the  instructions,  it  is  clear  that  he  cannot  grasp 
so  completely  as  its  author  the  scope  of  the  plan,  and  hence 
contradiction  and  confusion  might  ensue.  The  second 
person  might  not  have  the  same  feeling  of  responsibility 
for  the  imperfections  of  the  work  if  the  original  plan  were 
the  work  of  another.  (The  instructions  issued  by  the 
various  German  States  for  the  carrying  out  of  the  census 
of  industry  of  1875  :  Stat.  d.  D.  R.,  Bd.  XXXIV.,  Th.  I. 
S.  129  ff.) 

The  instructions  require  in  every  case  the  most  pains- 
taking preparation  and  supervision.  The  process  is  here 
entirely  bereft  of  any  theoretical  character  which  might  be 
seen  in  the  plan.  The  process  acquires  a  concrete  practical 
form.  The  logical  character  of  the  aggregates  and  units 
are  not  questions  for  the  enumerators.  The  area  is  sub- 
divided  into   smaller   portions,   provinces,   governmental 


176  Annals  of  the  American  Academy. 

districts,  tax  districts,  court  districts,  city,  county,  or 
election  districts,  districts  of  registration,  districts  of 
chambers  of  commerce,  army  districts,  and  others  suffi- 
ciently numerous.  Provision  must  be  made  that  the 
limits  are  not  misunderstood  or  overstepped.  In  excep- 
tional cases  of  common  or  disputed  jurisdiction  it  may  be 
necessary  to  come  to  some  conclusion.  (Stat.  d.  D.  R., 
Bd.  XIV.,  1874,  p.  I.  24,  §9.) 

The  subdivision  of  time  is  the  usual  one  of  years, 
months,  and  weeks.  When  the  condition  at  a  given 
moment  is  to  be  ascertained,  the  point  of  time  must  be 
carefully  noted. 

V  Theoretically,  a  single  instant  is  desired ;  practically,  this 
is  only  approximately  attainable.  Hence  it  becomes  neces- 
sary in  an  enumeration  of  population,  for  instance,  to  fix 
rules  for  distribution  and  collection  of  the  schedules,  for 
noting  the  seamen,  travellers,  the  newly-born,  and  dying, 
and  also  for  later  corrections  and  additions.  (Stat.  d.  D.  R., 
Bd.  I.  1873,  p.  75,  §§8,  10,  13,  16,  17.) 

Just  as  little  is  there  any  conscious  conception  of  the 
unit  of  enumeration  as  such.  The  things  themselves  are 
counted — persons,  houses,  and  wares — they  are  distin- 
guished by  sex,  conjugal  conditions,  age,  religion,  occu- 
pation, education ;  and  as  with  persons,  so  also  with  houses 
and  wares,  cultivation  and  crops,  phenomena  of  the  sky, 
and,  in  fact,  with  every  object  of  enumeration.  It  is,  as  a  rule, 
the  variable  qualities  of  typical  things  which  are  concerned. 
Here  are  all  the  difficulties  indicated  in  §  66.  The  idea 
which,  in  the  plan,  may  be  very  clear,  must  be  expressed 
as  briefly  and  definitely  as  possible,  yet  so  as  to  be  com- 
monly understood  without  difficulty.  This  is  the  labor  of 
the  expert,  and  cannot  be  relegated  to  another  person.  In 
particular,  provision  must  be  made  for  the  manner  in 
which  distinctions  of  measure,  size,  weight,  and  value  are 
to  be  made,  and  how  these  are  to  be  applied  to  the 
things  to  be  rendered  capable  of  enumeration  by  such 
distinctions  (§  65).     Further,  it   is   essential  to   consider 


Theory  and  Technique  of  Statistics.  177 

how  far  an  estimate  of  the  aggregate  may  take  the  place 
of  the  actual  measurement  of  such  qualities,  or  whether 
estimate  may  be  used  at  all  in  place  of  enumeration. 
Precise  instructions  are  particularly  requisite  in.  dealing 
with  things  which  are  susceptible  only  of  estimates  and 
not  of  actual  enumeration.  (Stat.  d.  D.  R.,  Bd.  XLIII. 
Th.  I.  p.  57,  and  Centralbl.  fur  d.  Deutsch  Reich.,  1879, 
p.  855  :  Distinctions  of  wares,  and  tare  percentages  in  sta- 
tistics of  trade.  Bd.  I.,  p.  102  :  Estimate  of  area  and  crops 
in  agricultural  statistics.) 

All  these  things  are  best  given  as  explanations  and 
directions  for  the  use  of  the  enumeration  schedule.  The 
body  which  directs  the  enumeration  immediately  or  in- 
directly cannot  dispense  with  instructions  covering  the 
entire  field,  giving  necessary  provisions  for  the  extent, 
organization,  the  initial  steps,  and  time-limits  of  the  pro- 
cess. When  intermediate  bodies  summarize  the  results,  in 
whole  or  in  part,  a  schedule  of  tabulations  is  necessary. 

The  directions  and  instructions  for  officials  and  enumer- 
ators assume  necessarily  the  character  and  structure  of  a 
law  or  regulation.  (Examples,  §  95.)  They  must  prevent 
dubious  or  conflicting  interpretation  in  all  details,  and  form 
an  objective  standard  for  those  who  make  and  those  who 
use  the  enumeration.  Whoever  undertakes  to  carry  out  the 
plan  or  to  use  the  material  gained  must  be  careful  not  to 
depart  from  the  instructions  and  the  characterizations  of 
the  objects  given  therein.  Criticism  is  directed  to  the  in- 
terpretation of  the  contents,  and  we  recognize  very  properly 
the  ability  of  the  statistical  expert  in  his  preparation  of 
exhaustive  unmistakable  instructions.  (Mittheilung  der  In- 
struktionen  §  21  der  Allgemeinen  Bestimmungen  in  betr. 
der  Volkszahlung  im  D.  R.,  Stat.  d.  D.  R.,  Bd.  I.,  p.  75 ; 
Neue  Folge,  Bd.  I.,  p.  2,  §  18.) 


178  Annals  of  the  American  Academy. 


II.  Enumeration. 

•      §  99.   ORGANIZATION   OF  THE  PROCESS. 

The  process  is  thoroughly  concrete.  It  requires  a  fixed 
organization,  observations,  and  the  summarization  and 
tabulation  of  the  results.  The  phases  of  the  process  are 
different  according  as  we  make  an  observation  of  a  fixed 
condition  or  a  movement. 

The  distinction  is  to  be  seen  at  the  outset  in  the  organ- 
ization of  the  more  important  undertakings.  If  the  sta- 
tistical bureau  does  not  itself  undertake  the  enumeration, 
it  takes  place  through  the  agency  of  various  organs  of  the 
general  administration.  Those  which  make  the  observa- 
tions directly  are  often  very  various  and  often  difficult  to 
select. 

The  enumeration  of  a  fixed  condition,  as  of  population, 
cattle,  ships,  etc.,  must  arrange  to  investigate  the  entire 
field  in  a  certain  limit  of  time.  The  mobility  of  the  ob- 
jects requires  a  rapid — as  nearly  as  possible  an  instantane- 
ous observation.  Close  relations  to  less  mobile  objects 
(buildings,  industries,  farms)  lead  to  the  enumeration  of 
the  latter  at  the  same  time.  Hence,  such  undertakings 
assume  large  proportions  and  require  large  numbers  of 
observers.  They  are  repeated  periodically.  In  conse- 
quence they  cannot  furnish  regular  employment,  and  it 
cannot  be  avoided  that  persons  without  preparation  and 
practice  should  be  employed.  Hence  there  is  great  neces- 
sity for  some  preparation  and  instruction.  The  plan  has 
recently  been  adopted,  where  the  degree  of  general  intelli- 
gence would  permit,  that  each  house-owner  or  mill-owner, 
and,  indeed,  all  heads  of  families  should  write  their  own 
answers  upon  a  list  or  card  containing  the  printed  ques- 
tions. The  enumerator  has  in  this  case  only  a  secondary 
function :  he  lends  his  assistance  in  case  of  doubt,  and 
merely  revises  the  results.      (Stat.  d.  D.  R.,  Bd.  XIV.  p. 


Theory  and  Technique  of  Statistics.  179 

I.  24,  §§  4-13,  18 ;  Bd.  XX.,  p.  I.,  72,  §§  7-9).  The  greater 
the  division  of  labor,  the  simpler  is  the  work  of  each  indi- 
vidual. It  may,  therefore,  be  possible,  as  in  Germany,  to 
secure  this  labor  from  persons  who,  in  consideration  of  the 
public  utility  of  the  work,  do  it  without  remuneration. 

The  chief  reliance  for  the  correctness  of  the  data  is  in 
any  case  the  good-will  and  interest  of  those  concerned. 
Means  to  facilitate  this  correctness  are  good  schedules, 
the  cooperation  and  supervision  of  experts,  rewards  which 
may  be  forfeited  by  neglect,  and  penalties  for  refusals  to 
make  returns  or  for  intentionally  false  returns.  (Reichs- 
gesetz  betr.  Berufsstatistik  vom  13  Februar,  1882,  §  5,  R. 
G.  Bl.  9.)  Finally,  we  must  include  in  many  cases  the 
self-interest  of  the  participants  as  members  of  the  com- 
munity. (Preussische  Gewerbesteuerollen,  Gesetz.  vom 
30  Mai,  1820,  Ges.  S.  133.  Gutereinschatzungen  der  land- 
wirthschaftlichen  Kreditvereine). 

Observations  of  movements  requiring  a  much  longer 
time  must  be  made  from  one  or  more  stations.  They  have 
a  more  complicated  character,  and  are  as  a  rule  conducted 
by  permanent  and  therefore  expert  observers.  (Registra- 
tion, Tax,  Customs,  Signal  Service  officials.) 

The  observation  is  greatly  facilitated  when  the  phenom- 
enon appears  periodically,  or  may  be  so  observed,  as  in 
the  case  of  meteorological  and  river-depth  observations. 
It  is  necessary  to  arrange  that,  at  every  point  when  an 
occurrence  of  the  phenomena  is  possible  there  should  be 
an  observer  present,  whose  attention  is  called  to  the  matter 
either  at  once  or  subsequently.  These  observers  must 
have  fixed  districts  in  order  to  avoid  omissions  and  dupli- 
cations, and  it  must  also  be  determined  whether  the 
double  occurrence  of  the  same  thing  is  to  be  noted  once 
or  twice.  (Statistik  des  Seeverkehrs,  Stat.  d.  D.  R.,  Bd.  L, 
p.  240,  §  5,  15.)  In  the  first  case  it  would  be  necessary  to 
distinguish  each  individual  by  name  or  mark  of  some 
kind  (§  67). 

In  addition  to  proper  organization  and  supervision,  good 


180  Annals  of  the  American  Academy. 

results  may  often  be  secured  by  the  requirements  of  the 
business  of  administrative  bureaus.  Such  are  obligations 
which  must  be  satisfied  by  money  payments  (taxes),  regis- 
tration, which,  if  neglected,  entails  fines  or  other  losses 
(births,  deaths,  etc.,  or  losses  which  are  to  be  made  good 
by  insurance);  finally,  also,  automatic  registers,  which 
require  only  periodical  supervision  (meteorological  and 
hydrographic  stations). 

(Examples  of  very  ingenious  aids  in  the  organization 
under  the  most  difficult  circumstances  are  to  be  found  in 
the  census  and  registration  in  East  India :  Report  on  the 
Census  of  British  India,  1881,  Vol.  3,  1883.) 

§  IOO.    THE   OBSERVATION    IN    ENUMERATIONS. 

The  observation  is  the  decisive  point  of  the  process.  It 
must  permeate  into  the  facts,  find  the  occurrence  of  the 
phenomena,  make  the  necessary  distinctions,  count  with- 
out omission  or  duplication,  so  that  a  correct  total  may  be 
obtained.  The  observation  is  based  upon  a  direct  and  sub- 
jective act  of  perception.  Theoretically,  the  statistical 
process  consists  of  a  succession  of  such  acts  with  sharp  and 
clear  distinctions,  but  the  technical  practice  assumes  a  very 
different  form. 

There  is  only  a  relatively  small  number  of  investigations 
in  which  the  enumerator  searches  for  the  phenomenon 
and  decides  what  shall  be  counted.  Under  ordinary  cir- 
cumstances it  includes  only  the  census  of  population  and 
domestic  animals,  and  these  only  in  the  most  primitive 
form  of  direct  observation.  Nowadays,  when  the  owners 
and  heads  of  families  make  out  the  lists  there  is  little  for 
the  enumerator  to  do.  The  observation  is  made  by  those 
who  answer  the  questions,  and  is  hardly  liable  to  mistakes 
as  to  the  facts,  but  only  to  misapprehension  of  the  ques- 
tions. 

In  many  matters  the  same  person  makes  the  observa- 
tion who  makes  the  statistical  tabulation.     But  these  per- 


Theory  and  Technique  of  Statistics.  181 

sons,  clergymen,  registrars,  assessors,  receivers  of  taxes, 
meteorologists,  make  these  observations  independently  of 
the  statistical  problems,  and  are  led  by  very  different  mo- 
tives to  devote  a  higher  degree  of  attention  and  care  than 
would  appear  were  statistical  considerations  the  only  reason 
for  their  labors.  By  far  the  greater  part  of  the  data,  from 
the  simplest  to  those  of  the  automatic  registers,  which  are 
useful  for  statistical  purposes,  do  not  belong  in  the  first 
instance  to  statistical  work.  Statistics  does  not,  as  a  rule, 
participate  in  the  observation,  but  makes  only  a  critical 
examination  of  the  results.  Hence  statistical  instructions 
rarely  devote  space  to  the  act  of  observation.  They  are 
concerned  more  with  the  proper  classification  of  objects 
already  observed  in  order  to  increase  their  usefulness 
or  statistical  problems. 

Certain  phenomena  (houses,  horses,  storms),  which  can 
readily  be  distinguished,  may  be  simply  counted  by  rely- 
ing upon  the  memory,  and  the  giving  the  total  for  the 
area  or  period.  Objects  of  a  more  variable  nature  cannot 
be  properly  counted  without  more  precise  methods.  This 
precision  may  be  obtained  simply  by  rubrics  in  which  each 
unit  when  observed  is  noted,  so  that  the  sum  of  the  nota- 
tions will  give  the  sum  of  the  corresponding  units.  If  we 
have  a  special  column  for  female,  for  single,  for  married, 
or  divorced  persons,  the  number  of  dots  or  lines  in  each 
column  will  give  the  number  of  each  class.  It  may  be 
desired  to  sum  up  the  distinctive'  qualifications  not  alone 
but  in  connection  with  each  larger  class  of  units  (e.g., 
divorced  women).  In  this  case  a  direct  count  is  possible 
only  for  the  larger  class  and  not  the  special  class.  The 
observation  of  the  distinctions  would  require  another  sepa- 
ration. Accordingly,  there  must  be  different  forms  of 
schedules  (§  68). 

If  qualifying  characteristics  are  introduced  in  the  sched- 
ules, and  the  number  of  each  is  found,  we  have  a  sum- 
marized view  of  the  observation.     The  final  summarization 
is  not  commenced.     All  these  things  are  independent  of 
13 


1 82  Annals  of  the  American  Academy. 

the  source  whence  the  data  are  gathered,  whether  from 
direct  observation,  from  reports  of  the  enumerated,  or  from 
the  numberless  lists  required  for  the  ordinary  purposes  of 
administration. 

§  10 1,  the  observation  in  estimates. 

When  estimates  and  calculations  are  brought  into  use 
instead  of  enumerations,  the  observation  assumes  a  totally 
different  aspect.  The  abridgment  of  the  statistical  process 
under  certain  circumstances  by  the  use  of  substitutes  for 
enumeration  has  already  been  discussed.  It  is  possible, 
and,  in  some  cases,  even  unavoidable  (§  69).  Theory  always 
requires  much  the  same  thing,  that  is,  the  determination 
of  the  units  in  the  aggregate.  Technically  the  difference 
is  very  great  if  enumeration  is  employed  or  a  substitute. 

In  one  case  the  estimate  attaches  to  a  certain  grouping 
in  the  condition  of  the  units,  which  is  supposed  to  be 
seen,  so  that  in  a  certain  sense  the  sums  are  observed  and 
counted.  Whether  the  groups  are  seen  or  remembered,  in 
every  case  a  portion  of  the  operation  of  enumeration  is 
dispensed  with.  Yet  the  object  is  considered  directly. 
Indirect  methods  may  be  employed  and  more  liberty 
allowed  in  making  the  estimate.  The  most  common  form 
is  the  conclusion  of  probability,  already  discussed  (§§  83, 
86).  The  known  results  in  analogous  cases  form  the  basis 
of  the  conclusion  which  judges  the  relation  of  the  unit  to 
the  aggregate  in  the  analogous  aggregates  to  be  identi- 
cal with  that  of  the  aggregate  to  be  investigated,  even 
when  nothing  is  known  of  the  latter  but  the  analogy. 
Such  estimates  are  of  universal  application.  No  one 
hesitates,  when  conditions  do  not  change,  to  estimate 
the  taxes,  crops,  prisoners,  railroad  traffic,  etc.,  of  a  coun- 
try by  the  figures  of  the  year  before.  Condorcet  very 
properly  declares  that  this  is  the  calculation  of  the  healthy 
human  intellect.     Nevertheless,  he  underestimates  the  im- 


Theory  and  Technique  of  Statistics.  183 

portance  of  complete  conformity  with  the  conditions  of 
the  method  for  absolute  accuracy. 

Estimates  may  also  be  made  without  a  complete  chain 
of  analogies.  In  those  cases  where  enumeration  presents 
very  great  difficulties  there  are  not  apt  to  be  any  enumer- 
ations for  analogous  aggregates.  Probability  cannot  be 
employed  where  the  interest  of  the  problem  attaches  to 
the  variations  within  the  same  individual.  Hence,  esti- 
mates can  be  made  on  the  testimony  of  experts. 

The  broad  field  of  economic  statistics  is  especially  de- 
pendent upon  such  estimates.  While  it  would  not  be 
impossible  to  determine  by  measurement,  by  enumeration, 
the  area  cultivated  with  the  different  agricultural  products, 
it  would  be  wholly  impracticable.  Estimates  are  usually 
required  from  local  authorities,  who  may  employ  more  or 
less  complicated  methods.  But  it  is  impossible  to  know 
by  enumeration  the  harvest  by  grain  and  straw,  roots,  or 
hay.  This  would  require  for  each  large  and  small  farm, 
data  which  the  farmer  himself  could  not  furnish  with  any 
accuracy.  For  such  purposes  there  is  no  other  resource 
than  the  average  estimates  of  experts.  (Stat.  d.  D.  R.,  Bd. 
I.,  S.  103;  Motive,  p.  116.)  Similar  conditions  apply  in 
the  statistics  of  industry  and  trade.  The  product  of  manu- 
factures and  the  profits  of  tradesmen  could  be  enumerated, 
for  they  are  in  the  books.  But  like  the  tax  office,  statis- 
tics must  be  content  with  estimates.  Even  when  the  ques- 
tion is  asked  directly  of  the  producers,  their  replies  are 
largely  estimates  or  supplemented  by  estimates  (e.  g.y 
Montanstatistik,  Stat.  d.  D.  R.,  Bd.  I.,  p.  302,  Bd.  XXX., 
L.  12,  55;  Bd.  I.,  Neue  Folge,  p.  53).  Consumption  and 
production,  wages,  prices  charged  by  mechanics,  small 
traders,  carriers,  etc.,  are  susceptible  only  of  estimate. 

The  process  is  apparently  most  simple,  for  the  expert  is 
simply  asked  his  opinion.  But  this  opinion  is  the  fruit  of 
complicated  processes.  Unless  he  can  base  it  upon  enu- 
meration, a  direct  survey  of  the  groupings  or  analogies, 
he  must  resort  to  indirect  methods.     He  may  find  some 


1 84  Annals  of  the  American  Academy. 

support  in  the  numerical  relations  of  some  other  object 
which  includes  the  object  in  question,  or  bears  some 
causal  relation  to  it,  or  is  in  some  other  way  symptomatic 
of  it.  Experience  or  experiment  will  guide  him  in  estab- 
lishing a  relation  for  the  usual  connection  of  the  two  ob- 
jects, as,  for  instance,  a  relation  of  the  harvest  to  the 
kinds  of  crop,  or  of  the  product  in  a  spinnery  to  the 
spindles  when  the  area  of  cultivation  and  the  number  of 
spindles  is  known.  As  the  application  to  the  absolute 
total  is  simple,  the  main  question  is  often  as  to  the  rela- 
tion. The  expert  knows  by  calculation  that  x  distilled 
liquor  tax  indicates  y  mash  mass.  Hence,  he  infers  that 
in  a  given  district  the  distilleries  use  potatoes  of  z  quality, 
with  /  exploitation.  Hence,  from  the  amount  of  tax,  he 
can  tell  the  consumption  of  potatoes  for  the  given  district 
and  period.  It  is  to  be  noted  that  his  judgment  holds 
good  only  for  the  given  district  and  year. 

Yet  in  this  method  there  is  always  a  certain  definite 
course  which  the  expert  must  pursue  in  his  observation. 
He  must  give  an  average  relation.  He  must  have  sufficient 
knowledge  not  only  of  one  or  of  some  cases,  but  of  so 
many  that  he  may  assume,  as  in  the  case  of  probabilities, 
to  have  a  just  appreciation  of  the  fluctuations  between  the 
maximum  and  minimum  and  of  their  approximate  rela- 
tion. According  to  circumstances  this  feeling  may  be 
justified  as  based  upon  causal  technical  or  economic  con- 
nections of  a  very  definite  nature,  and  thus  the  estimate 
be  very  accurate.  On  the  contrary,  accuracy  in  the  esti- 
mate may  require  such  a  series  of  observations,  that,  like 
an  enumeration,  all  the  phenomena  in  question  must  be 
drawn  into  consideration  singly,  or  at  least  in  groups. 

This  shows  the  limits  of  the  application  of  the  processes 
of  estimate  and  enquete  (§  69).  It  is  impossible  even  from 
the  most  accurate  observation  of  single  cases,  or  of  a  por- 
tion of  the  field  to  be  investigated,  to  form  a  judgment  of 
the  totality  of  the  phenomena  or  of  the  entire  field,  unless 
it  may  be  shown,  and  this  ought,  as  a  rule,  to  be  proven, 


Theory  and  Technique  of  Statistics'.  185 

that  the  totality  of  the  phenomena  and  the  entire  field 
possess  everywhere  like  conditions  and  relations. 

§  102.   SUMMARIZING. 

The  result  of  the  observation,  by  whatever  method  it 
may  have  been  gained,  is  expressed  in  the  number  of  units 
found  in  the  aggregate.  The  summarization  must  include 
the  sums  and  all  the  distinct  subdivisions  required  by  the 
instructions. 

When,  in  simple  cases,  the  observer  simply  gives  the 
total  for  his  district,  or  they  are  gathered  from  his  lists, 
the  summarization  consists  only  in  the  complete  total  of 
all  the  districts. 

In  some  cases  the  units  cannot  be  added  in  the  collec- 
tion schedules,  as  they  require  separation  for  the  distinc- 
tions. In  this  case  a  large  schedule  in  shape  of  the  tabu- 
lation schedule  is  prepared,  and  the  data  from  the  lists 
gathered  under  the  proper  titles  by  scoring  for  each  case  a 
vertical  line  with  the  customary  horizontal  line  for  the  fifth 
or  tenth  case,  so  that  the  total  can  readily  be  obtained. 
If  the  distinctions  are  very  numerous  this  process  is  very 
inconvenient  and  tedious.  The  paper  is  large,  the  proper 
column  must  be  found,  errors  are  apt  to  be  frequent  and 
the  method  therefore  unreliable. 

Since  i860,  therefore,  enumeration  cards  have  come  into 
use.  They  were  originally  introduced  in  Italy,  and  1867 
in  Prussia  (Zeitschr.  d.  Preuss.  Stat.  Bureaus  VII.,  1867,  p. 
305)  in  the  following  form  :  For  each  unit  in  the  collection 
schedule  a  card  was  prepared  from  the  lists  giving  all  the 
qualifications  in  the  shortest  possible  form.  A  further  step 
was  to  give  such  cards  to  the  heads  of  families  for  them 
to  fill  out,  one  for  each  member  of  the  household.  This 
was  introduced  into  the  general  German  census  of  1871 
for  Prussia,  Lauenburg,  Brunswick,  and  Hamburg,  through 
the  efforts  of  Engel.  The  simplification  of  the  clerical 
work  has  led  to  its  use  in  various  fields  (Stat.  d.  D.  R.,  Bd. 


1 86  Annals  of  the  American  Academy. 

II.  p.  112;  Nessmann,  in  Zeitschr.  d.  Preus.  Stat.  Bureaus, 
i8;i,p.  271). 

With  the  cards  the  distinctions  are  summarized  simply 
by  placing  cards  with  like  data  in  piles,  and  then  counting 
the  cards.  In  this  placing  and  counting  it  is  easy  to 
attain  great  manual  dexterity.  Each  pile  can  now  be 
used  for  any  number  of  other  distinctions.  The  more 
numerous  such  combinations  the  greater  must  be  the 
economy  of  time  and  cost  which  is  gained  by  cards  in 
preference  to  the  older  method. 

(Appendix  IV.  shows  seven  comparatively  simple  combi- 
nations as  to  population.  Including  the  ten  columns  omitted 
for  women,  it  would  require  in  an  ordinary  schedule  823 
columns  to  be  filled  and  counted.  In  these  there  would  be 
for  every  1000  persons  9000  entries.  By  the  card  method 
a  single  sorting  and  counting  for  each  combination,  i.  e., 
by  sorting  and  counting  7000  cards  the  same  result  can 
be  obtained  more  accurately  and  in  one-third  of  the  time. 
The  explanations  in  the  Appendix  show  how  the  cards 
are  to  be  grouped  and  counted,  after  which  counts  they 
are  to  be  thrown  together  again.) 

As  is  shown  by  Appendix  V.,  cards  may  be  made  which 
give  not  only  the  sums  by  counting  them  off,  but  which 
also  give  the  sums  in  such  a  way  that  by  placing  one  over 
the  other  they  may  be  added  up  without  further  additional 
writing. 

In  all  summarization,  from  the  simplest  to  the  most  com- 
plex, the  rule  holds  that  no  opportunity  should  be  lost  to 
prove  the  results  obtained.  The  figures  should  be  so 
arranged  that  sums  of  certain  lines  when  added  give  the 
same  results  as  the  sums  of  certain  columns,  and  thus  all 
error  avoided.     (See  Appendix  IV.) 

The  grand  total  gives  the  final  results  as  to  the  aggre- 
gate enumerated.  It  must  always  be  looked  upon  as  a 
desirable  elaboration  of  the  result  when  the  aggregate  is 
divided  (§  90)  in  the  summarization  into  as  many  as  pos- 
sible appropriate  portions.    It  has  already  been  seen  (§  74) 


Theory  and  Technique  of  Statistics.  187 

that  such  portions  have  the  value  and  character  of  smaller 
aggregates,  only  when  in  them  exactly  the  same  units  have 
been  observed  as  in  the  general  aggregate.     If  there  are  1 

data  which  do  not  unite  to  form  aggregates,  they  are 
important  only  as  accessory  numbers  for  calculations. 

Every  complete  summarization  needs,  according  to  the  (^ 
requirements  of  the  theory,  an  explanatory  statement  as  to 
the  instructions,  the  mode  of  carrying  them  out,  the  effect 
of  any  deviation  from  the  rules,  and  the  presumptive  de- 
gree of  correctness  of  the  result.  This  is  necessary  for  the 
critique.  The  latter  can  be  much  more  effective  when  the 
original  data  are  given.  (Preuss.  Statistik,  Heft  XXXIX., 
2  Februar,  1882,  p.  65  ;  Gutachten  der  K.  Bezirksverwal- 
tungsbehorden,  Stat.  d.  D.  R.,  Neue  Folge,  Bd.  I.  p.  53; 
Montanstatistik  Bestimmungen,  §  5  et  seq.) 

III.  Examination  of  Returns.       Qp 

§  IO3.    EXAMINATION,    CORRECTION,   AND   CRITICISM 
OF   THE   RESULT. 

The  examination  of  the  returns  is  necessary  in  order  to 
assimilate  the  matter  to  the  plan,  so  that  the  conclusions 
necessary  to  answer  the  question  may  be  drawn  from  it. 
It  requires  that  the  result  of  the  new  enumeration  be\ 
critically  examined  and  ascertained  exactly,  that  the  anal- 
ogous aggregates  suitable  for  comparison  should  be  ex- 
amined and  arranged  for  that  purpose,  and  finally  that  the 
results  be  reduced  to  ratios. 

The  basis  of  all  further  discussion  is  the  degree  of  ac- 
curacy which  may  properly  be  ascribed  to  the  results  of 
the  enumeration.  It  is  indispensable  therefore  to  determine 
from  the  standpoint  of  the  most  rigid  practical  statistician 
whether  in  reality  the  process  has  conformed  to  the  plan 
and  instructions,  whether  also  the  instructions  issued  have 
entirely  agreed  with  the  intentions  of  the  plan;  further, 


1 88  Annals  of  the  American  Academy. 

whether  the  organization  and  capacity  of  enumerators  and 
experts  was  adequate  to  a  proper  and  reliable  observation, 
and  finally,  whether,  in  counting  up,  no  deficiencies  and 
ambiguities  have  crept  into  the  result.  It  is  necessary,  as 
far  as  the  material  allows,  to  test  the  clearness  of  each 
return  and  the  mathematical  accuracy  of  each  calcu- 
lation. 

Besides  such  formal  investigation  there  must  be  a  con- 
tinuous and  attentive  criticism  of  the  figures,  testing  at 
every  step  their  probability.  A  basis  for  such  compari- 
son may  be  found  by  calculation  from  typical  relations. 
Within  the  results  of  the  same  enumeration  a  careful 
sifting  of  the  matter  will  show  deviating  relations  which 
were  to  be  expected,  and  also  concentration  or  scarcity 
for  which  there  is  no  explanation.  Finally,  the  compari- 
son with  the  results  for  earlier  years,  or  for  analogous 
aggregates,  even  those  only  remotely  related,  leads  us  to 
be  sceptical  of  particularly  large  differences  for  which  no 
reason  is  apparent. 

Such  matters  must  be  cleared  up  by  subsequent  re- 
search and  the  mistakes  corrected.  Any  subsequent  enu- 
meration which  may  be  necessary  for  such  corrections 
must  obviously  take  place  with  reference  to  the  same 
period  as  the  chief  enumeration.  (Stat.  d.  D.  R.,  Bd.  I., 
Neue  Folge,  p.  2,  §  12.)  Unquestionable  errors  can  only 
be  omitted;  or,  when  no  other  means  are  at  hand,  be 
removed  by  proper  explanations. 

After  careful  application  of  all  these  sifting  processes  it 
remains  to  ascertain  the  totals  which  are  to  be  considered 
the  final  results. 

Errors  are  in  any  case  unavoidable.  It  has  often  been 
proposed  to  express  this  in.  the  numbers  themselves  by 
giving  only  round  numbers.  Without  doubt  the  feeling  of 
security  is  increased  by  using  only  the  unquestionable 
figures,  e.  g.,  the  first  three  places  of  every  number.  This 
would  indicate  that  possible  mistakes  were  considered  as 
less  than  one  per  cent.      But  even  if  such  percentages 


Theory  and  Technique  of  Statistics.  189 

could  always  be  given,  the  correctness  of  the  number 
would  obviously  not  be  enhanced.  Rounding-off  the 
numbers  always  brings  an  increase  or  decrease,  and  the 
actual  number  seems  preferable  to  this,  and  has  greater 
probability. 

Nevertheless,  as  already  shown  (§  70),  a  judgment  must 
be  made  as  to  the  presumptive  possibility  of  error  in  order 
to  use  the  number's  at  all  for  the  present  problem.  How 
far  this  may  be  necessary  for  other  problems  should,  unless 
the  possibility  of  error  is  very  small,  be  definitely  explained 
and  recorded  for  the  future  student  of  the  material.  Up  to 
a  certain  point  it  is  necessary  to  accord  a  certain  amount 
of  credence  to  the  authority  of  the  expert  who  prepares  a 
statistical  investigation.  He  should  therefore  be  fully  alive 
to  the  responsibilities  of  his  position. 


§  IO4.    THE   COMPARISON    WITH    ANALOGIES. 

When,  possibly  after  considerable  labor,  the  numbers 
have  been  obtained,  no  further  progress  has  been  made 
than  the  indefinite  description  pointed  out  in  §  73.  There 
is  as  yet  no  fixed  method  by  which  a  judgment  may  be 
formed  until  a  comparison  with  other  and  analogous 
aggregates  has  been  made.  The  comparison  is  the  same, 
no  matter  what  kind  of  judgment  the  problem  requires. 
Preceding  paragraphs  (§§  82  and  86)  have  shown  that  all 
probability  depends  upon  previously  ascertained  causality, 
and  this  upon  quantity.  Hence,  whatever  the  ultimate  end 
may  be,  the  first  step  in  drawing  conclusions  from  the  data 
is  a  judgment  of  quantitative  relations. 

Yet  this  first  step  is  partially  conditioned  by  the  ultimate 
purpose.  Every  series  of  analogous  masses  in  which  like 
units  have  been  counted  will  enable  us  to  establish  quan- 
titative ratios  which  are  unimpeachable  in  their  form. 
They  may  have  a  value  for  certain  judgments.  For  this 
reason  caution  is  needed  in  using  the  large  mass  of  the 


190  Annals  of  the  American  Academy. 

systematic  material  described  in  §90.  While  ratios  and 
comparisons  are  frequently  prepared  for  the  aggregates 
and  units  of  these  comprehensive  schemes,  it  should  be 
remembered  that  a  slight  variation  of  the  question  (§91) 
often  suffices  to  change  the  analogy  completely  and  render 
the  former  comparison  useless. 

In  a  special  problem  there  is  always  a  special  question 
which  must  be  precisely  stated  and  clearly  comprehended. 
This  shows  where  we  must  look  for  the  materials  for  the 
comparison  necessary  in  quantitative  judgments.  Unless 
complete  agreement  in  the  analogy  of  the  masses  is  se- 
cured the  agreement  of  the  units  will  not  fit  them  for 
comparison.  Whether  the  analogies  belong  to  a  large 
number  of  simultaneously  counted  aggregates  or  are 
drawn  from  widely  different  periods  or  localities  is  of  no 
consequence,  either  for  the  underlying  idea  and  method 
of  comparison  or  for  its  technical  treatment. 

If  quantitative  relations  may  be  judged  from  such  com- 
parisons the  second  question  of  causality  may  perhaps  be 
answered.  It  requires  for  its  conclusions  certain  additional 
independent  premises,  for  which  the  analogies  must  be 
found,  examined,  and  compared,  even  though  they  may 
exist  in  the  same  aggregate.  In  similar  fashion  the  judg- 
ment of  probability  or  regularity  requires  a  third  technically 
distinct  arrangement  of  the  problem. 

Each  of  these  forms  corresponds  to  a  certain  syllogism. 
They  depend  upon  the  enumeration  of  exactly  the  same 
units  in  entirely  analogous  aggregates  and  upon  sufficient 
accuracy  in  the  process.  They  all  need  critical  examina- 
tion of  the  results.  This  examination  must  go  over  all 
the  points  which  would  be  important  for  a  new  enumera- 
tion, and  must  test  particularly  whether  the  method  of 
enumeration  or  estimate,  applied  possibly  with  a  totally 
different  end  in  view,  does  not  contain  too  large  a  margin 
of  error  for  the  problem  in  hand. 

However  large  or  small  the  group  of  analogies  applica- 
ble to  the  comparison,  it  should  always  admit  technically 


Theory  and  Technique  of  Statistics.  191 

of  a  systematic  review,  in  which  the  aggregates  and  units, 
with  their  distinctions  and  their  limitations,  and  with  their 
totals,  should  clearly  appear. 


§  IO5.  REDUCTION   TO    RATIOS   FOR   COMPARISON. 

Once  decided  that  the  aggregates  and  units  are  capable 
of  comparison,  the  only  further  step  is  to  reduce  them  to 
common  terms  (§  76).  For  each  comparison  the  series  in 
which  the  maxima,  minima,  and  fluctuations  may  be  rec- 
ognized and  the  average  made,  can  only  be  derived  from 
the  same  measure. 

This  reduction  is  a  purely  arithmetical  operation,  and  it 
is  entirely  immaterial  whether  the  final  purpose  may  be  a 
judgment  of  quantitative  relations  or  a  search  for  causality 
and  probability  among  more  complex  conditions.  But  it 
is  an  essential  factor,  a  connecting  link  between  the  ma- 
terial and  the  solution. 

As  a  rule,  all  these  reductions  determine  the  number  in 
which  the  units  are  found  on  an  average  in  equal  divisions 
of  time  or  space,  or  how  many  units  of  one  kind  are  found 
for  a  fixed  number  of  another  in  the  aggregates  compared. 
The  mode  of  calculation  in  the  principal  cases  has  already 
been  indicated  in  §  j6.  Very  complicated  calculations  may 
be  necessary  in  these  reductions.  Theoretically  all  ele- 
ments of  the  reduction,  e.  g.y  the  area  of  the  aggregates, 
must  be  collected  with  the  fundamental  material.  This  is 
not  always  the  case  in  fact,  for  it  may  be  necessary  to  make 
a  special  inquiry  for  certain  elements  to  make  the  reduc- 
tion complete.  Technically  this  is  important,  as  it  is  not 
probably  the  concern  of  the  usual  organization  (§  99),  but 
requires  a  special  process  to  be  united,  as  a  rule,  with  the 
labors  of  the  statistical  organs. 

Such  special  inquiries  are  all  the  more  necessary,  as  it 
is  not  always  easily  foreseen  what  points  of  view  may  be 
most  suitable  for  comparison  in  conclusions  of  causality 


192  Annals  of  the  American  Academy. 

and  probability.  In  some  larger  undertakings  (production, 
trade,  and  similar  subjects)  series  of  units  may  occur,  some 
of  which  are  noted  by  weight,  some  by  piece,  some  by 
measure,  and  which  can  be  compared  only  when  reduced 
to  value  or  some  other  common  term.  Thus  arises  the 
necessity  of  the  determination  of  price,  value,  or  other 
matters,  the  possible  intricacy  of  which  was  indicated  in 
the  allusion  to  the  statistics  of  trade  in  §  93. 

The  similarity  of  the  units  may  be  so  conceived,  that 
though  obtainable  from  the  material,  they  may  require 
very  extensive  calculations.  An  example  is  to  be  found 
in  the  death  tables  mentioned  in  §93,  when  the  problem 
is  to  compare  the  average  life  of  the  populations  of  differ- 
ent States  and  periods.  A  similar  case  is  the  comparison 
of  different  districts  with  reference  to  the  medical  aid 
within  the  reach  of  each  inhabitant.     (Stat.  d.  D.  R.,  Bd. 

XXV..  1877,  §  57-) 

Even  when  these  complicated  methods  do  not  enter  into 
the  question,  the  reduction  of  a  large  number  of  totals  may 
require  a  multitude  of  multiplications  and  divisions,  and 
involve  the  expenditure  of  a  great  deal  of  labor.  Hence 
various  technical  devices  are  employed  to  facilitate  the 
work. 

Multiplication  tables  are  useful  when  the  same  figures 
are  used  often  as  multipliers  or  divisors.  For  variable 
figures  the  Calculation  Tables  of  A.  L.  Crelles  (1858), 
"  which  save  all  multiplication  and  division  of  figures  less 
than  1000,"  are  of  service;  also  tables  of  logarithms,  with 
seven  figures  (v.  Vega,  Bremiker),  or  five  figures  (Bremi- 
ker,  Albrecht,  Schloemilch),  or  even  four  figures  (Witt- 
stein).  Calculating  machines  render  good  service.  Various 
constructions  have  been  tried ;  the  most  satisfactory  is  the 
Arithmometer.  It  was  invented  by  Thomas,  of  Strassburg, 
in  1820;  produced  at  a  moderate  price  in  185 1  (240  mark), 
and  has  since  1880  been  quite  generally  adopted  in  the 
more  important  bureaus.' 


Theory  and  Technique  of  Statistics.  193 


IV.   The  Presentation  of  the  Results. 

§  106.  requirements  of  the  presentation. 

Whoever  has  examined  the  material,  and  compared  the 
analogous  aggregates  after  their  reduction  to  common 
terms,  is  in  a  position  to  give,  if  possible,  a  solution  of 
the  problem.  The  ratios  show  at  once  the  quantitative 
relations  for  the  aggregate  investigated,  what  causalities 
may  be  considered  as  predominant,  and  in  what  number 
the  phenomena  are  to  be  expected. 

On  the  basis  of  these  simple  mathematical  relations  the 
statistician  is  frequently  able  to  solve  at  a  glance  many 
statistical  problems.  This  depends,  of  course,  on  the  na- 
ture and  accessibility  of  the  material.  No  scientific  propo- 
sitions can  be  based  on  the  conclusions  of  a  single  observer, 
however  capable  he  may  be.  The  specialist  is  often  able 
to  answer  the  questions  from  his  general  knowledge  of 
the  premises,  and  frequently  he  would  hardly  need  the 
reduction  to  ratios.  But  if  his  labors  are  to  be  beyond 
question,  and  to  have  lasting  value,  he  cannot  omit  to 
present  his  material  and  the  whole  process  of  proof  in 
such  a  way  that  any  sufficiently  informed  person  might 
convince  himself  of  the  correctness  and  reliability  of  the 
conclusions,  and  find  the  solution  himself. 

This  presentation  is  essentially  a  report  on  such  portions 
of  the  process  as  may  be  necessary  to  establish  the  proof 
and  furnish  the  means  of  testing  it.  The  facts  must  be 
brought  out  as  completely  as  possible,  so  arranged  as  to 
show  their  connection  with  the  problem.  The  entire  means 
of  proof  should  be  exhibited,  and  with  them  the  calcula- 
tions upon  which  it  is  based.  The  wealth  of  material 
even  for  the  most  ordinary  problems  would  make  de- 
mands almost  impossible  of  fulfilment  in  meeting  these 
requirements,  were  it  not  that  the  method  of  statistics 
furnishes  peculiar  simplifications  whose  importance  seems 
to  be  scarcely  adequately  appreciated. 


194  Annals  of  the  American  Academy. 

The  strictly  logical  character  of  statistical  investigation 
permits  the  presentation  of  statistics  in  an  admirably  clear 
and  simple  form.  Statistical  investigation  deals  with  real 
facts,  but  by  mean's  of  familiar  ideas.  On  the  basis  of 
these  ideas  it  measures,  sifts,  and  systematizes  the  object 
investigated.  Nothing  not  included  in  these  ideas  attracts 
attention,  and  just  as  the  scheme  groups  the  ideas  with 
their  distinctions,  their  species  and  genera,  so  the  conclu- 
sions can  also  be  similarly  collected.  Nothing  in  the 
ideas  is  changed.  All  that  is  new  is  the  number  of  things 
corresponding  to  each  found  by  observation.  Hence  a 
special  form  for  statistical  proof  is  possible  which  presents 
with  the  utmost  precision  and  brevity  the  enormous  num- 
ber of  varying  qualities  which  have  been  ascertained.  This 
is  done  by  representing  the  logical  interdependence  of  the 
ideas  in  the  manner  of  presentation.  This  gives  rise  to 
tabulation  and  graphical  representation. 

§  107.    TABULATION. 

The  tabular  presentation  gives  a  complete  account  of 
the  entire  process  by  giving  concisely  the  results  of  each 
step.  The  table  gives  briefly  the  ideas  outlined  in  the 
plan.  The  tabular  system  is  best  applied  when  the  hori- 
zontal lines  are  devoted  to  the  aggregates,  the  vertical 
columns  to  the  various  units.  The  various  aggregates 
are  named  at  the  beginning  of  the  line,  the  units  at  the 
head  of  the  column.  When  the  meaning  of  the  terms 
used  to  designate  the  units  needs  further  explanation,  a 
note  containing  extracts  from  the  instructions  serves  the 
purpose  best. 

The  numbers  for  units  of  the  same  sort  are  therefore 
placed  one  above  the  other.  There  can  be  no  doubt  of 
the  meaning  of  the  totals,  and  the  eye  detects  differences 
readily  in  the  figures  where  units,  tens,  hundreds  are  in 
the  same  vertical  line.  If  reduced  to  ratios,  the  latter 
may   be   introduced   into   parallel   columns  of  the  same 


Theory  and  Technique  of  Statistics.  195 

scheme,  and  the  comparison  made  without  further  effort. 
It  is  useful  also  to  place  in  the  table  the  area  or  size  of  the 
aggregates,  and  this  occurs  generally  in  the  column  im- 
mediately after  the  names.  Logically  also  a  fixed  portion 
of  the  area  is  like  an  enumerated  unit,  and  the  total  area 
a  total  of  enumerated  units. 

All  columns  except  those  containing  ratios  furnish  totals. 
These  are  the  total  number  of  the  units  of  the  same  kind 
found  in  all  the  aggregates  compared.  Brought  into  a 
ratio  with  a  total  of  the  sizes,  we  have  the  average  of  the 
ratios  by  which  the  individual  ratios  may  be  measured. 
In  the  same  way  units  which  form  part  of  a  larger  unit 
may  be  compared,  and  the  percentual  relations  of  their 
totals  to  the  total  of  the  larger  unit  determined. 

All  tabular  presentations  have  similar  contents.  It  is 
only  a  difference  of  form  when  the  aggregates  are  in  the 
columns,  the  units  on  the  lines,  but  it  is  not  so  clear.  The 
case  is  different  when  the  aggregate  is  divided  by  position 
and  size  on  the  lines  and  by  time  in  the  columns.  In  this 
case  the  table  can  only  include  the  figures  for  a  single  unit. 
In  like  manner  the  columns  may  be  occupied  by  various 
units  and  the  lines  by  their  distinctions,  or  the  reverse.  In 
this  case  the  table  can  only  include  a  single  aggregate,  and 
the  comparison  is  more  difficult,  as  each  aggregate  needs 
a  separate  table.  Such  tables,  however,  show  more  clearly 
the  influences  of  changes  in  the  aggregates  and  the  special 
relations  of  the  same  units. 

§  108.    GRAPHICAL   PRESENTATION. 

Graphical  presentation  is  a  modification  of  the  idea  under- 
lying the  tables.  It  uses  geometrical  instead  of  numerical 
methods.  It  often  shows  the  results  in  their  geographical 
distribution  instead  of  merely  naming  the  sections  as  in  a 
table.  The  object  is  to  gain  greater  clearness  and  simplify 
the  drawing  of  conclusions. 

It  is  perfectly  clear  that,  for  every  unit  or  100  units,  a 


196  Annals  of  the  American  Academy. 

point,  a  line,  or  a  small  surface  might  be  placed  in  the 
system  of  coordinates.  (Appendix  VI.  b.  c.  a.)  If  the 
number  is  to  be  expressed  by  a  line,  it  is,  as  a  rule, 
measured  upon  a  vertical  line  from  a  fixed  horizontal  line, 
and  for  the  sake  of  greater  clearness  the  points  are  united. 
One  can  distinguish  subdivisions  of  a  larger  unit  by  differ- 
ent color  or  shading  of  the  proportionate  part  of  the  line 
or  surface. 

Instead  of  drawing  the  lines  perpendicular  to  a  fixed  line, 
they  can  be  drawn  from  one  point  as  radii  and  the  surfaces 
may  be  colored.  Surfaces  may  be  indicated  in  squares,  and 
shading  or  coloring  be  employed  to  indicate  subdivisions. 
In  each  square  a  system  of  coordinates  may  be  placed. 
But  the  further  this  goes  the  more  the  simplicity  which  is 
the  prime  object  is  lost.  All  such  methods  of  indicating 
sizes  are  called  diagrams. 

Hexagrams  and  chronograms  are  similar  plans  of  show- 
ing the  intensity  of  a  phenomenon  at  various  periods  of 
time,  by  the  rise  and  fall  of  a  curve  within  a  system  of 
coordinates  expressing  a  measure  and  time.  If  this  occurs 
in  an  automatic  register,  observation  and  representation 
take  place  simultaneously.  But  the  hexagram  may  also 
be  constructed  later. 

A  chorogram  is  the  result  when  different  aggregates  are 
indicated  by  surfaces,  showing  the  size  of  each,  and  por- 
tions of  the  surface  are  colored  or  shaded  differently  to 
indicate  the  result  of  the  enumeration  in  each  aggregate. 
It  can  be  profitably  employed  to  show  the  different  degrees 
of  the  occurrence  of  a  single  phenomenon  in  different 
aggregates. 

Cartograms  are  representations  in  which  the  geographi- 
cal map  shows  the  totals  or  the  ratios  of  the  different  units 
by  various  inserted  diagrams  and  hexagrams.  The  dia- 
grams may  here  show  a  certain  number  of  distinctions,  but 
the  limit  is  soon  reached.     (G.  Mayr:  Marey,  §  57.) 

In  recent  times  solids  have  been  used  for  these  purposes. 
They  have  the  advantage  of  three  dimensions  instead  of 


Theory  and  Technique  of  Statistics.  197 

two.  But  the  difficulty  of  constructing  them,  reproducing 
and  preserving  them,  make  an  extended  use  of  them 
impracticable.     (Perozzo,  §  57.) 

§  IO9.     DEMONSTRATION    OF    THE   QUANTITATIVE  JUDGMENTS. 

The  demonstration  follows  almost  mathematically  from 
the  presentation.  It  is  based  upon  the  certainty  that  an 
analogy  exists  between  the  aggregate  which  has  been  in- 
vestigated and  those  with  which  it  is  compared,  and  that 
in  all  of  them  the  things  in  question  have  been  counted  or 
estimated  sufficiently  accurately.  This  must  be  beyond  a 
doubt,  or  else  any  further  step  is  impossible.  No  one 
should  omit  to  elucidate  the  means  of  examination  by  an 
explanation  of  the  plan,  of  the  instructions,  the  results, 
and  the  possibility  of  error. 

Under  the  supposition  that  all  requisites  are  complied 
with,  the  aggregates  and  the  totals  of  enumerated  things 
become  merely  quantities  whose  concrete  character  is  not 
drawn  into  consideration.  Conclusions  are  based  on  num- 
ber and  measure,  on  the  mutual  connections  and  relations 
of  these  comparable  quantitative  notions. 

The  regular  statistical  process  advances  from  the  de- 
scriptive material  to  a  judgment  of  quantity,  of  causality, 
and  probability.  Practical  demonstrations  must  follow  the 
same  course.  In  each  special  case  it  is  a  question  at  what 
point  the  problem  in  hand  receives  the  solution  desired. 
Circumstances  may  make  the  path  longer  or  shorter,  but 
its  direction  is  always  the  same. 

The  demonstration  finds  a  like  expression  in  every  ex- 
ample, but  is  perhaps  clearest  in  the  graphic  presentation.. 
For  our  explanation  a  case  in  which,  as  in  Appendix  VI.,, 
prominent  extremes  occur,  will  render  the  most  efficient 
service.  Suppose  that  for  the  investigation  presented  in 
Appendix  VI.  attention  were  called  to  the  phenomena  of 
the  week  ending  June  10,  1876,  in  the  city  B,  and  that 
within  the  limits  of  time  and  space  thus  indicated,  the 
14 


198  Annals  of  the  American  Academy. 

deaths  be  considered  worthy  of  special  observation.  We 
find  in  the  delineation  of  the  problem  in  column  23  not 
only  the  unit  d,  deaths  of  all  kinds,  but  a  number  of  others 
which  have  been  subject  to  observation  and  enumeration. 
Such  are  in  the  first  instance  parts  of  the  unit  d  specially 
noted,  as  i  deaths  of  children  under  one  year  of  age,  / 
deaths  from  zymotic  and  epidemic  diseases  (typhoid  fevers, 
dysentery,  diphtheria,  measles,  etc.),  and  finally  as  a  sub- 
division of  the  last,  m  the  deaths  from  measles  alone. 
Other  contemporaneous  phenomena  are  also  observed, 
evidently  with  the  idea  that  they  might  have  some  con- 
nection with  the  deaths.  Such  are  :  a,  the  rainfall ;  b,  in- 
tensity of  the  wind,  and  c,  the  direction  of  the  wind;  e, 
the  atmospheric  pressure ;  f,  the  atmospheric  temperature; 
g,  the  level  of  flowing  water ;  h,  of  subterranean  water ; 
and  finally,  k,  the  price  of  rye.  That  the  winds,  observed 
three  times  daily  as  to  direction,  and  the  price  of  rye  are 
not  observed  specially  for  the  week  in  column  23,  but 
only  for  the  month  of  June,  is  a  defect.  These  data  refer 
to  a  larger  aggregate,  the  portion  of  which  belonging  to 
the  aggregate  23  cannot  be  determined.  Yet  it  must  be 
assumed  that  any  possible  connection  between  the  aggre- 
gate 23  and  these  factors  is  to  be  considered  sufficiently 
characterized  by  the  figures  for  the  month. 

It  needs  no  further  explanation  to  demonstrate  that  from 
the  total  d,  observed  for  the  aggregate  23,  or  from  the  sum 
of  the  units  a  to  et  no  one  could  know  whether  they  were 
large  or  small.  This  question  could  only  be  answered  by 
comparison  with  the  aggregates  1  to  52.  Here  it  is  clear 
that  it  is  a  question  of  the  place  of  the  week  June  4-  10  in 
relation  to  the  rest  of  the  year.  If  one  wished  to  compare 
the  week  June  4-10  with  previous  years  in  the  same  city 
or  of  other  cities  in  respect  to  the  units,  the  analogy  would 
be  quite  different,  and  hence  also  the  standard  of  com- 
parison. 

A  survey  of  the  unit  d  in  the  various  aggregates  to  be 
compared  shows  at  once  that  23  has  the  maximum  num- 


Theory  and  Technique  of  Statistics.  199 

ber.  The  final  column  shows  the  average  for  the  year. 
By  extending  this  average  line  across  the  page  the  fluc- 
tuations to  each  side  would  be  apparent.  The  question 
of  the  quantity  of  the  unit  d  in  the  aggregate  23  may  be 
answered,  therefore,  by  saying  that  it  exceeds  the  average 
by  nearly  half;  that  like  extremes  occur  only  in  the  aggre- 
gates 31  to  34,  while,  as  a  rule,  the  fluctuations  including 
those  toward  the  minimum  are  much  smaller. 

In  a  similar  manner  the  other  units  may  be  measured 
by  reference  to  the  standard  given  by  the  average  for 
each,  noting  the  deviation  from  the  mean.  Thus,  it  ap- 
pears that  in  23,  besides  d,  the  units  a,  5,/,  i,  /,  and  m 
occur  in  unusual  strength,  whereas  the  deviation  from  the 
average  for  the  units  c,  e,  g,  h,  and  k  is  scarcely  appreci- 
able. 

This  is  the  basis  of  an  exact,  if  not  very  far-reaching 
judgment  as  to  the  quantitative  relation  of  the  units.  The 
treatment  of  the  material  could  not  differ  essentially  if 
the  aggregate  23  represented  a  year  of  large  exports,  a 
district  with  large  or  small  crops,  or  any  other  field  of 
observation. 

Whether  the  data  for  the  various  aggregates  are  the 
result  of  systematic  statistical  efforts  collected  for  a  special 
purpose,  possibly  even  by  means  of  estimate,  would  not, 
apart  from  the  possibility  of  error,  affect  the  mode  of  rea- 
soning in  the  slightest.  Nor  would  it  be  changed  if 
instead  of  a  single  aggregate  the  entire  field  were  the 
subject  of  the  judgment  (§  90). 

§  1 10.   THE     DEMONSTRATION    OF    JUDGMENTS    OF    CAUSALITY 
AND    PROBABILITY. 

If  the  problem  is  not  limited  merely  to  quantity  but 
includes  also  causality,  the  demonstration  must  consider 
the  different  sets  of  phenomena  in  turn.  Suppose  the 
question  to  be  the  cause  of  the  extreme  phenomena  of 
the  aggregate  23.     One  might  at  first  look  for  k,  the  price 


200  Annals  of  the  American  Academy. 

of  rye,  which  might  possibly  indicate  scarcity  of  food,  and 
if  so  a  probable  cause  of  high  death-rate.  A  close  exam- 
ination excludes  this  presumption  entirely.  The  price  of 
rye  is  subject  to  slight  variations,  and  it  is  observed  that 
in  the  aggregates  compared  the  mortality  is  lowest  when 
the  price  is  highest. 

The  influence  of  epidemics  is  a  possible  cause.  But  the 
unit  m  does  not  prove  it.  It  does  show  the  maximum  of 
deaths  from  measles,  which  may  be  considered  epidemic. 
It  shows  the  relation  of  this  disease  to  all  diseases  of  the 
class.  The  deaths,  /,  caused  by  epidemic  and  zymotic  dis- 
eases, have,  apart  from  the  deaths  from  measles,  a  compara- 
tively uniform  and  slight  relation  to  the  general  mortality 
from  the  beginning  of  January  to  the  middle  of  July,  and 
again  from  the  middle  of  September  to  the  end  of  Decem- 
ber. It  is  only  for  the  aggregates  29  to  35  that  an  exces- 
sive increase  of  the  zymotic  and  epidemic  mortality  is 
noticed,  but  it  is  observed  that  measles  have  no  part  in  it. 
If,  however,  we  consider  the  causality  of  the  sum  m  for  the 
sum  d  in  the  aggregate  23,  it  is  plain  that  m,  mortality 
from  measles,  gives  no  satisfactory  explanation.  Thirty- 
six  deaths  in  m  subtracted  from  235  in  d,  leave  still  47  in 
excess  of  the  average  154,  a  difference  almost  equivalent 
to  the  extreme  minimum  (154-93). 

Further  explanation  is  necessary,  and  it  may,  perhaps, 
be  found  in  the  infant  mortality.  With  an  average  of  62 
it  shows  in  23  the  large  number  of  102.  But  it  is  com- 
monly known  that  measles  are  fatal  chiefly  to  children. 
If  we  subtract  the  mortality  from  that  source  we  find  that 
the  infant  mortality  has  not  appreciably  increased. 

Instead,  therefore,  of  special  influences,  we  must  look  to 
more  general  climatic  relations.  From  the  units  g  and  ht 
which  indicate  the  humidity  of  the  soil,  it  appears  that 
there  is  no  reason  to  suppose  miasmatic  influences,  which 
would  have  shown  themselves  in  an  increase  of  zymotic 
and  epidemic  diseases.  The  subterranean  water  at  47.8 
dm.  above  low- water  mark  is  higher  than  the  average,  46.2. 


Theory  and  Technique  of  Statistics.  201 

This,  with  the  flowing  water,  which  at  59.9  dm.  is  higher 
than  the  average,  50.5,  prevents  the  dangerous  drying-up 
of  the  ground.  The  atmospheric  pressure  e  is  evidently 
indifferent,  as  it  corresponds  exactly  to  the  average,  331, 
Parisian  scale,  or  29.397+  inches.1  Observing  the  direc- 
tion of  the  wind,  it  is  noticeable  that  no  southwest  wind 
occurred,  yet  the  others  are  all  in  about  the  average  pro- 
portion. Of  more  weight  is  the  fact  that,  as  shown  by  bt 
it  was  less  intense  than  in  the  other  summer  months.  On 
the  other  hand  it  is  not  markedly  below  the  average.  The 
rainfall,  a,  of  the  week  23  is  slight,  only  one-sixth  of  the 
average.  But  it  can  scarcely  be  looked  upon  as  a  cause 
of  sickness,  for  though  the  preceding  week  had  only 
one-third  of  the  average,  the  one  before  that  had  had  a 
precipitation  of  three  times  the  average  of  9.3  Parisian 
scale.  Among  all  the  elements  prepared  for  this  investi- 
gation there  remains  only  the  atmospheric  temperature. 
This  does,  indeed,  show  very  extreme  conditions.  The 
weekly  average  is  the  highest  of  all.  The  maximum  of 
23. 90  R.  is  only  once  exceeded,  in  the  30th  week,  which 
shows  26.20  R.,  and  the  minimum  of  -f-io.6°  R.  is  only  a 
little  less  than  the  minimum  of  week  30.  A  peculiar  feat- 
ure is  that  the  high  temperature  was  developed  very  rap- 
idly from  a  comparatively  low  one.  In  the  middle  of  May 
the  mean  temperature  was  less  than  the  yearly  average — 
the  minimum  was  — 1°  R.  and  the  maximum  only  -f-  12.20 
R.  Hence,  the  change  was  very  sudden.  The  effect  of 
this  abrupt  change  seems  to  be  indicated  by  the  increase 
of  measles. 

This  investigation  would  evidently  be  defective  if  the  in- 
ductive or  experimental  knowledge  which  has  been  called 
in  so  largely  to  furnish  premises  could  point  out  any  other 
more  probable  general  or  special  circumstance  as  the  cause 
of  the  increase  of  mortality  in  the  week  in  question.  It 
would  then  have  been  necessary  to  measure  these  influ- 

1  In  the  Parisian  scale  405.3425  =36  inches. 


202  Annals  of  the  American  Academy. 

ences  by  enumeration  either  directly  or  by  means  of 
symptoms.  If  a  critique  does  not  indicate  such  circum- 
stances, it  must  be  admitted  that  the  quantitative  relations 
adduced  in  the  presentation  clearly  show  the  rapidly  in- 
creasing temperature  to  be  the  cause  of  the  great  mortality 
in  the  aggregate  23. 

It  is  perfectly  clear  that  the  material  which  is  prepared 
for  such  a  proof  of  causality  is  capable  of  furnishing  other 
similar  proofs.  The  Appendix  VI.  shows  in  the  extremes 
31  and  34,  already  mentioned,  another  easily  perceptible 
causality.  A  general  view  of  the  course  of  the  lines 
shows  that  here  the  zymotic  and  epidemic  diseases  are  the 
cause,  and  more  precisely,  among  children  under  one  year. 
In  spite  of  the  enormous  increase  of  the  mortality,  the 
deaths  of  those  of  more  advanced  years  show  great  regu- 
larity from  the  week  24  to  the  end  of  the  year.  All  fluc- 
tuations in  this  part  of  the  year  are  caused  by  the  infant 
mortality,  which  is  zymotic — epidemic,  yet  not  attributable 
to  measles.  We  must  exclude  as  a  cause  of  the  fatality  of 
disease  in  31  to  34,  apart  from  dearness  (k),  also  atmos- 
pheric pressure  (e)  and  wind  (b,  c).  On  the  contrary,  the 
subterranean  water  (k)  shows  an  obviously  unfavorable 
status.  It  has  sunk  from  a  level  above  the  average  to  2  dm. 
below,  and  at  the  same  time  the  flowing  water  shows  the 
lowest  position,  2  dm.  below  the  level  of  the  subterranean 
water.  Dangerous  miasmas  are  highly  probable.  Never- 
theless, the  first  extreme  of  high  mortality  precedes  this 
sinking  of  the  water-level.  Yet  the  second  extreme  may 
have  been  partly  due  to  this  cause.  Again,  the  chief  cause 
appears  to  be  the  temperature,  rendered  less  endurable  by 
long  drought  and  feeble  winds.  The  deaths  are  distin- 
guishable from  those  of  the  week  23  in  having  a  zymotic 
and  epidemic  character,  but  without  measles. 

Besides  these  causal  connections  the  presentation  illus- 
trates in  the  34th  week  another.  It  is  in  the  obvious 
reason  for  the  remarkably  rapid  decrease  of  zymotic  and 
epidemic  mortality,  which  with  the  infant  mortality  sinks 


Theory  and  Technique  of  Statistics.  203 

in  the  three  weeks  34,  35  and  36,  the  greatest  extreme,  to 
a  point  below  the  average.  The  reason  is  the  excessive 
rainfall  of  the  week  34.  The  temperature  does  not  seem 
to  have  been  cooled  off  enough  to  account  for  the  decrease. 
The  explanation  is  the  direct  purification  of  the  atmosphere 
and  the  closing  of  the  pores  of  the  earth  by  the  great 
amount  of  rain. 

If  it  is  possible  by  such  means  to  arrive  not  only  at  a 
negative  result,  that  causes  cannot  be  proved,  but,  in  spite 
of  the  highly  hypothetical  character  of  the  conclusions,  to 
reach  a  satisfactory  positive  result,  there  is  no  need  of  any 
special  demonstration  that  it  is  possible  and  desirable  to 
pursue  the  matter  further  to  conclusions  of  probability. 
Under  like  conditions  for  two  aggregates,  a  cause  proved  to  , 
be  operative  in  the  one  may  properly  be  supposed  to  cause 
the  like  effect  in  the  other,  and  its  intensity  may  be  meas- 
ured by  the  intensity  of  the  effect,  compared  with  analo- 
gous aggregates.  No  one  can  doubt  that  an  increased  dry 
heat  will  increase  the  fatality  of  sickness,  or  that  sharp 
and  continuous  rains  will  purify  the  air  more  effectually 
than  weaker  ones.  According  to  the  nature  of  the  causal 
connection  and  the  thing  in  question,  the  expression  of 
such  a  relation  in  a  definite  number  is  more  or  less  ven- 
turesome, yet  if  it  is  a  question  of  using  it  statistically  it 
must  be  done,  always  making  ample  reservation  for  the 
possible  margin  of  error.  With  properly  prepared  mate- 
rial this  is  always  possible.  The  entire  presentation  deals 
with  definite  quantities,  and  a  relatively  most  probable 
quantity  can,  of  course,  be  calculated  from  them.  The 
causality  in  Appendix  III.  shows  that  with  rye  at  9.6  mk. 
a  hectolitre,  an  average  of  861  marriages  per  100,000  in- 
habitants is  the  most  probable  for  the  four  countries. 
By  interpolation,  according  to  the  scale  of  absolute  fig- 
ures, the  most  probable  number  can  be  deduced  for  other 
rye  prices,  provided  that  with  such  defective  material  as 
the  determination  of  price  can  (§  65)  furnish,  they  may 
seem  to  have  value.     To  develop  from  probabilities  the 


204  Annals  of  the  American  Academy. 

regularities  cannot  be  considered  the  concern  of  the  single 
problem  and  its  proof. 

§  III.    CHARACTER   OF   THE   SOLUTION. 

Presentation  and  proof  furnish  the  answer  which  is  the 
solution  of  the  problem.  The  importance  of  the  solution 
must  not  be  overestimated.  The  peculiar  processes  of 
statistical  methods  fix  very  definite  limits  for  the  result. 
The  problem  requires  an  observation  from  a  certain  point 
of  view  of  a  variable  and  confused  aggregate,  definite  only 
in  its  limits.  Corresponding  observations  were  made  in 
similar  aggregates.  Whether  the  question  concerns  a 
single  aggregate  or  a  great  number  making  up  a  total  is 
wholly  unimportant.  It  is  only  essential  that  the  observa- 
tion should  be  made  with  the  use  of  the  same  logical 
premises. 

These  observations  furnish  the  basis  for  all  conclusions 
which  have  facilitated  in  any  way  the  solution.  Hence,  it 
is  clear  that  the  latter  is  limited,  as  already  seen  (§91),  to 
these  fundamental  premises.  It  rests  strictly  within  the 
definite  boundaries  of  time  and  space  of  the  compared 
aggregates  and  of  the  characteristics  of  the  things  ob- 
served, forming  the  units  of  enumeration.  This  holds 
also  in  the  field  of  probability.  It  cannot  extend  beyond 
the  limits  traced  by  the  conditions.  This  limitation  fol- 
lows, as  a  matter  of  course,  from  §§  82  and  86,  for  proba- 
bilities are  only  a  species  of  proportion,  where  three 
known  factors  furnish  a  fourth.  In  like  manner  every- 
thing claiming  to  be  a  regularity  is,  as  explained  in  §  $6, 
always  dependent  on  the  analogy  of  the  aggregates.  Rules 
for  the  occurrence  of  qualities  of  things  may  be  estab- 
lished inductively  and  experimentally  with  more  or  less 
precision,  and  the  mutual  relations  of  different  things  may 
be  marked  out.  Such  rules  are  derived  from  the  general 
nature  of  the  things,  as  shown  by  observation  and  experi- 
ment.    Such  a  rule  is  not  statistical.     Statistics  can  only 


Theory  and  Technique  of  Statistics.  205 

be  based  upon  the  fact  that  a  given  combination  of  things 
has  been  observed  under  like  conditions  in  a  great  number 
of  aggregates,  and  hence  under  essentially  unchanged 
conditions  the  same  combination  may  be  expected  in  an- 
alogous aggregates. 

Where  definite  concrete  things,  such  as  cultivation  and 
crops,  trade,  transportation,  finance,  tax  statistics,  and  the 
like  are  concerned,  this  limitation  is  at  once  apparent. 
But  in  problems  of  a  somev/hat  more  abstract  character 
the  tendency  to  generalize  is  always  dangerous. 

For  the  validity  of  a  rule  the  confirmation  of  numerous 
examples  is  more  decisive,  but  the  presumption  of  a  regu- 
larity appears  admissible  from  such  problems  and  presen- 
tations as  Appendix  III.  In  this  problem  the  price  of  rye 
is  properly  taken  as  a  symptom  of  the  cost  of  daily  sub- 
sistence, and  the  rule  is  that  cheap  bread  renders  marriage 
easier.  But  whoever  would  conclude,  for  instance,  that 
with  900  marriages  per  100,000  inhabitants  cheap  subsist- 
ence, and  with  700  dear  subsistence,  were  to  be  inferred, 
would  entirely  overlook  the  fact  that  the  question,  whether 
the  average  861  marriages  per  100,000  inhabitants  was  many 
or  little,  was  at  the  most  answered  only  for  the  four  states 
in  question ;  that  for  other  countries  they  furnish  no  stan- 
dard. That  the  price  of  rye  is  not  claimed  to  be  a  standard 
for  the  cost  of  living  in  remote  lands  hardly  needs  to 
be  mentioned.  Anyone  who  would  conclude  from  the 
decrease  of  the  price  of  rye,  an  increase  for  example  of 
marriages  among  peasants,  might  be  taught  exactly  the 
opposite  by  actual  enumeration.  The  problem  concerns 
only  the  total  population,  and  does  not  indicate  how  the 
price  of  rye  may  affect  single  classes. 

That  no  characteristics  of  the  unit  may  be  changed,  that 
none  may  be  neglected  and  none  added,  and  that  every 
more  abstract  or  general  conception  includes  such  change, 
is  more  obvious.  Much  difficulty  arises,  for  instance,  from 
the  use  of  the  term  city  instead  of  city  district,  in  enu- 
merations of  population  and  the  like. 


206  Annals  of  the  American  Academy. 

Just  as  little  should  the  great  importance  of  the  solu- 
tions obtained  be  underestimated.  The  entire  history  of 
statistics  is  a  steadily  increasing  testimony  to  its  useful- 
ness and  indispensability.  Its  utility  has  been  shown  only 
within  the  limits  in  which  alone  it  can  be  true.  It  is  no 
fault  that  it  cannot  fulfil  demands  and  expectations  which 
have  no  foundation  in  those  simple  and  logical  premises 
which  should  be  clear  to  everyone.  Its  methods  and 
technique  have  always  been  aimed  at  the  mark  of  reliable 
observations.  Every  empirical  science  seeks  to  increase 
its  treasure,  and  each  finds  it,  in  spite  of  progress,  poorer 
than  desirable.  Like  the  controversy  of  1806  (§27),  it 
would  only  be  an  illusion  to  see  in  this  limitation  of  sta- 
tistics an  abandonment  of  ideal  aims.  The  demands  of 
that  day  were  simply  that  the  judgment  of  statistical  ag- 
gregates might  not  be  extended  to  combinations  of  phan- 
tasy until  it  stood  firmly  on  the  ground  of  measured 
facts. 

V.  Preservation  and  Application  of  the  Results. 

§  1 1 2.    COLLECTION   OF   THE     RICHEST     POSSIBLE     MATERIALS. 

The  last  requisite  of  statistical  technique  is  the  proper 
preservation  of  the  results  attained  in  the  treatment  of 
statistical  problems.  The  solution  of  every  scientific 
problem  is  of  permanent  value.  It  does  not  disappear 
with  the  immediate  occasion  for  it,  and  so  statistics  must 
furnish  lasting  achievements  for  the  further  development 
of  systematic  knowledge.  This  is  all  the  more  indispens- 
able in  statistics,  as  its  technique  requires  so  frequently 
the  use  of  earlier  results,  which  cannot  be  obtained  by 
subsequent  inquiries. 

This  demand  may  mean  preserving  the  original  mate- 
rial ;  i.  e.,  the  original  lists,  schedules  of  arrangement,  and 
collation,  with  the  necessary  explanations  (§  68),  and  in 
many  cases  this  must  suffice.     But  the  purpose  can  only 


Theory  and  Technique  of  Statistics.  207 

be  satisfactorily  obtained  by  printing.  Only  by  such  mul- 
tiplication of  the  results  obtained  is  a  proper  use  of  the 
material  possible,  a  comprehensible  and  handy  form  at- 
tained, and  the  occasional  whole  or  partial  destruction 
with  which  manuscripts  are  always  threatened  averted. 
The  presentation  (§§  106,  107)  takes  into  consideration  the 
printing  with  reference  to  the  contents  and  form.  With 
the  publication  the  work  becomes  public  property. 

Just  as  with  the  collection  of  the  material,  so  with  its 
preservation,  systematic  provision  has  very  fruitful  results. 
The  useful  results  of  one's  own  investigations,  as  well  as 
those  of  other  persons  and  other  periods,  are  collected, 
and  placed  in  readiness  for  possible  use.  So  far  as 
practicable,  scholars  and  scientific  and  private  institutions 
should  attempt  this  for  the  material  in  which  they  are  in- 
terested. But  it  is  the  province  of  the  State,  which  in  the 
nature  of  things  has  far  the  greater  number  of  statistical 
needs  and  functions,  to  provide  also  for  the  preservation  of 
statistical  material.  There  are  some  general  maxims  to 
be  considered  for  the  organization  of  these  official  collec- 
tions of  materials. 

§113.    THE   ARCHIVES    OF   OFFICIAL   BUREAUS. 

Each  State  endeavors  to  build  up  a  system  of  official 
statistics,  as  explained  in  §  88,  which  shall  be  appropriate 
to  its  own  conditions,  as  extensive  and  as  logically  con- 
nected as  possible.  At  the  same  time  the  official  bureau 
must  endeavor  not  to  lose  any  statistical  results  which  are 
carried  through  by  correct  methods  and  are  capable  of 
critical  estimate.  This  must  extend  to  private  statistics 
and  the  more  important  publications  of  foreign  States. 

It  is  necessary  in  the  first  place  that  the  appropriate  ma- 
terial which  may  exist  at  home  or  abroad  should  be  known 
to  the  bureau.  The  greater  part  of  the  statistical  publica- 
tions does  not  come  into  the  book  trade,  or  excites  so 
little  attention  that  it  is  not  noticed  in  advertisements  and 


208  Annals  of  the  American  Academy. 

catalogues.  The  reason  is  the  very  general  custom  of 
exchanges  between  the  various  institutions,  which  has  the 
effect  that  few  copies  are  sold.  It  would  be  wholly  unde- 
sirable to  change  this.  But  attention  must  be  given  first 
to  such  publications  as  are  not  exchanged,  and  second  to 
the  regularity  and  extension  of  the  exchanges.  Instruc- 
tions to  the  various  public  organs  to  send  in  their  publi- 
cations may  be  necessary.  At  the  same  time  the  purchase 
of  works  of  reference  and  compendiums  upon  all  branches 
of  economics  and  technology,  technical  dictionaries  and 
lexica  of  foreign  languages,  also  copies  of  statutes  and 
regulations,  and  particularly  of  the  best  and  most  complete 
topographic  charts,  is  indispensable.  This  material  in- 
creases from  year  to  year  in  bulk,  and  the  older  material 
has  lasting  value  for  statistics.  Provision  must  always  be 
made  for  an  appropriate  space  for  the  reception  and  classi- 
fication of  the  material  and  its  storage. 

Not  only  the  collection  of  the  material,  but  provision  for 
its  easy  accessibility,  is  very  important.  Catalogues  should 
include  not  only  the  title  but  also  the  main  points  of  the 
contents,  which  are  often  very  much  mixed  and  dissimilar 
in  the  same  work  ;  also  the  more  important  essays,  and  so 
forth,  that  they  may  be  easily  found.  (Preussisch.  Statist. 
Bureau,  Katalog,  see  §  50;  Zeitschrift,  Jahrgang  XX., 
1880.     Beilage.) 

The  less  the  official  statistician  is,  as  a  rule,  in  a  position 
to  draw  conclusions  from  the  statistical  matter  on  account 
of  the  necessary  work  of  preparation,  correction,  and  pub- 
lication, the  more  he  must  desire  to  see  such  scientific 
treatment  accomplished  by  private  persons  and  scholars. 
Yet  such  investigations  need  not  be  expected,  and  are  for 
the  greater  part  impossible  if  the  archives  are  merely  open 
to  investigators,  but  like  ordinary  libraries  presuppose  a 
knowledge  of  the  works  in  those  who  look  for  them.  They 
should  rather  be  arranged  like  historical  archives.  There 
should  be  well-informed  persons  who  are,  if  desired,  will- 
ing to  point  out  the  material,  and  when  necessary  to  ex- 


Theory  and  Technique  of  Statistics.  209 

plain  it.     (v.  Scheel,  Organisation  der  amtlichen  Statistik, 
1869). 

§114.    APPLIED   STATISTICS,    POLITICAL  ARITHMETIC. 

The  limits  of  exact  data  and  of  the  conclusions  which 
may  be  drawn  from  statistical  problems  have  been  shown  in 
§  1 1 1.  It  may,  however,  appear  that  the  limits  of  the  statis- 
tical field  have  been  drawn  too  closely,  if  certain  combina- 
tions commonly  designated  as  applied  statistics  or  political 
arithmetic  are  not  drawn  into  consideration.  These  are 
based  essentially  upon  the  union  of  numerical  results  and 
other  empirical  maxims,  with  strictly  statistical  data.  It 
would,  however,  be  hopeless  to  look  here  for  any  peculiar 
form  of  knowledge.  Inductive  and  experimental  knowl- 
edge as  well  as  deductions  come  into  play.  From  the 
interweaving  of  such  typical  relations  and  comprehensive 
abstractions  with  statistical  results,  rich  and  fertile  fields  of 
inquiry  may  arise. 

What  is  understood  by  political  arithmetic  founded  by 
Petty  (§  13)  is  chiefly  an  extension  of  statistical  enumera- 
tions and  probabilities  by  calculations  based  upon  techni- 
cally necessary  or  typical  relations.  When  the  number 
and  variety  of  the  ships  of  a  nation  have  been  statistically 
ascertained,  any  seaman  can  easily  tell  how  large  must  be 
the  crews  and  also  the  seafaring  population  of  the  nation. 
The  technical  expert  can  tell  easily  the  consumption  of  raw 
material,  the  necessary  machines,  the  approximate  produc- 
tion, the  circulating  capital,  and  other  essential  conditions 
of  the  enterprise  from  the  number  of  spindles.  Obviously 
all  these  data  come  by  calculation  from  the  empirical 
knowledge  of  the  person  who  makes  them  and  from  the 
premise  that  the  conditions  estimated  have  necessary  and 
typical  relations. 

The  combinations  can,  on  the  other  hand,  be  of  a  more 
abstract  nature.  Say  said,  that  without  the  aid  of  statistics 
political  economy  would  scarcely  be  an  empirical  science. 


210  Annals  of  the  American  Academy. 

This  is  not  correct,  as  Say  meant  it,  that  if  statistics  gives 
the  causes  or  effects  of  its  facts,  it  becomes  political  econ- 
omy. Yet  political  economy  has  two  sources  whence  its 
principles  are  drawn.  Either  the  typical  characteristics  of 
a  number  of  private  economies  which  have  been  observed 
are  applied  to  the  nation,  a  course  which,  on  account  of  the 
differences  of  economic  and  ethical  qualities  of  individuals, 
is  ambiguous  and  unreliable,  or  it  gains  them  by  the  enu- 
meration or  estimate  of  direct  or  symptomatic  phenomena 
within  the  entire  nation  or  of  so  much  as  is  concerned, 
i.  e.t  statistically.  The  latter  can  alone  give  an  exact  basis 
for  further  abstractions.  In  the  same  way  geography, 
history,  and  other  sciences  include  facts  statistically  ascer- 
tained and  abstractions  from  these  facts. 

The  scientific  conception  of  statistics  is  of  the  utmost 
importance  in  this  union  of  inductive  and  statistical  con- 
clusions. If  it  is  considered  the  science  of  a  certain  object 
one  must  either  include  all  objects  participating  in  such 
combinations  in  the  limits  of  statistics,  or  else  draw  a  line 
when  the  consideration  of  an  object  ceases  to  be  statistical 
and  belongs  to  another  science,  and  the  statistical  data 
utilized  are  to  be  looked  upon  as  subsidiary  to  the  latter. 

If  we  consider  statistics  from  a  standpoint  of  a  method 
which  examines  its  objects  from  a  point  of  view  closed  to 
other  methods,  then  the  single  problem  of  applied  statistics 
becomes  simply  a  portion  of  empirical  knowledge  investi- 
gated more  or  less  by  statistical  processes. 


CONCLUSION. 

§115.    THE   CHARACTER   OF  STATISTICAL  THEORY. 

It  has  been  demonstrated  that  ever  since  the  beginning 
of  history  extensive  statistical  investigations  were  requisites 
of  political  and  social  life,  and  how  in  consequence  an- 


Theory  and  Technique  of  Statistics.  211 

tiquity  and  the  middle  ages  show  in  various  fields  of  prac- 
tice some  empirical  skill.  Scientific  statistics  is  also  the 
immediate  outgrowth  of  the  practical  needs  of  State  and 
Church  in  modern  times.  They  existed  for  a  long  time  as  a 
mass  of  unconnected  and  partly  heterogeneous  matter,  until 
it  came  within  the  mighty  revolution  of  ideas,  which  since 
the  beginning  of  our  century  has  permeated  and  clarified 
all  scientific  knov/ledge.  The  idea  of  unity  in  the  entire 
field  of  scientific  statistical  activity  brought  with  it  also  the 
consciousness  of  a  peculiar  statistical  method.  The  tre- 
mendous development  of  statistics  in  public  administration, 
as  well  as  in  many  departments  of  economics  and  other 
sciences,  went  hand  in  hand  with  a  clearer  perception  of 
correct  and  exact  processes.  In  spite  of  the  most  diver- 
gent views  as  to  the  scientific  position  of  statistics,  there 
exists  entire  unanimity  among  statisticians  as  to  the  de- 
mands and  conditions  of  the  statistical  method] 

Our  presentation  of  the  subject  has  aimed  to  explain 
this  method  in  its  logical  foundation  and  in  its  technical 
application,  in  order  thus  to  gain  the  principles  of  an  un- 
ambiguous and  complete  theory  of  statistics.  The  result 
of  thjs  treatment  may  be  briefly  summarized.  Theoretical 
statistics  is  the  doctrine  of  a  strictly  systematic  process  of 
investigation  which  can  be  properly  applied  to  every  con- 
crete object  conceived  as  complex  and  changeable.  Sta- 
tistics is  capable  of  furnishing  knowledge  attainable  in  no 
other  way  as  to  the  connections  and  relations  of  things  in 
this  changing  aggregate.  This  doctrine  constitutes  a  well 
ordered  system  of  ideas,  demands,  and  principles  which 
have  definite  relations  to  the  general  theory  of  perception. 

Whatever  position  may  therefore  be  accorded  to  statistics 
in  a  system  of  the  sciences,  it  cannot  be  denied  that  un- 
less it  is  considered,  with  Sigwart  (§  58),  as  a  part  or  branch 
of  logic,  it  must  be  classed  properly  with  logic  and  mathe- 
matics, or  at  least,  as  is  done  by  Rumelin  (§  57)  and 
Haushofer,  with  the  methodical  sciences  of  critique  and 
hermeneutics. 


212  Annals  of  the  American  Academy. 

A  peculiarity  of  the  method  is  the  fact  that  its  compre- 
\  hension  is  not  based  upon  a  particular  portion  of  previous 
knowledge.  Although  for  many  problems  it  may  be  neces- 
sary to  have  very  exact  knowledge  of  political  and  legal 
matters,  or  of  technical  purposes  and  conditions,  kinds 
and  denominations  of  means,  tools,  and  materials  em- 
ployed, and  also  of  the  decisive  relation  of  the  events,  it 
is  not  in  all  these  cases  any  special  technical  knowledge 
that  is  required,  but  simply  just  such  ideas  and  points  of 
view  as  are  not  inaccessible  to  a  man  of  general  education 
and  common  sense. 

But  just  from  this  fact  very  appreciable  difficulties  arise. 
Because  statistics  operates  almost  exclusively  with  the 
ideas  of  everyday  life  and  combinations  of  numbers,  which 
are  very  simple,  it  makes  very  extraordinary  demands 
upon  the  specialist.  It  is  unfavorable  in  the  first  place 
that  the  purpose  of  the  problem  is  abstract,  that  it  is  not 
connected  with  the  direct  operations  of  daily  life.  It  cer- 
tainly is  very  interesting  to  compose  a  plan,  to  propose 
problems,  or  to  draw  or  substantiate  conclusions — but 
these  operations  are  rare  exceptions.  As  a  rule,  one  is 
concerned  simply  with  the  treatment  of  the  material,  col- 
lation, sifting,  and  correction  of  the  results,  continued  for 
years.  One  list  looks  like  another;  there  are  the  same 
ideas,  the  same  sets  of  figures  through  hundreds  of  sheets, 
always  the  same  common-place  things  and  everyday  dis- 
tinctions. At  the  same  time  we  must  not  overlook  any 
possible  misapprehension  of  the  idea  of  the  unit  of  enu- 
meration, whatever  form  it  may  assume,  nor  any  improba- 
bility in  the  data  which  may  include  errors.  Assistants 
may  indeed  be  charged  with  the  discovery  of  false  or 
changing  designations  of  things,  of  errors  of  calculation, 
of  writing,  etc.  But  all  more  serious  doubts  are  the  con- 
cern of  the  interest,  attention,  and  continued  patience  of  the 
specialist  properly  so-called.  Hence  it  is  obvious  that  any 
proposed  lightening  of  these  labors  involves  not  a  merely 
personal  question,  but  possibly  the  value  of  the  result. 


Theory  and  Technique  of  Statistics.  213 

On  the  other  hand,  because  it  deals  in  ideas  plain  to 
everybody  and  in  figures  which  are  easily  comprehended, 
statistics  is,  more  than  other  sciences,  subjected  to  mislead- 
ing and  trivial  use  and  criticism.  Because  of  its  simple 
elements,  its  conclusion  and  data  always  assume  a  form  of 
expression  apparently  comprehensible.  Interpreted  solely 
by  one's  general  knowledge,  changed  in  its  form  and  re- 
peated in  this  new  shape,  it  can  only  be  a  case  of  luck 
that  the  careful  choice  and  limitation  of  the  ideas  still  is 
applicable.  Yet  the  entire  system  of  conclusions  is  based 
upon  this  fact.  Often  when  doubt  arises  as  to  the  correct- 
ness of  such  traditions,  the  means  of  corroboration  are 
lacking,  and  even  when  these  are  known  nothing  is  easier 
than  falling  into  new  errors  by  small  mistakes  which  so 
easily  occur,  unless  there  is  a  certain  consciousness  of  the 
requirements  of  criticism  and  the  mode  in  which  the  data 
are  presented.  Hence  arises  that  peculiar  contradiction 
in  the  opinions  held  as  to  the  value  of  statistics,  that  one 
doubts  completely  the  value  of  the  figures,  and  another 
expects  from  statistics  what  is  unattainable. 

The  means  of  decreasing  these  unfavorable  conditions 
are  worthy,  finally,  of  our  attention. 

§Il6.    THE   WORK   OF  THE   PROFESSIONAL  STATISTICIAN. 

That  statistics  in  its  methods  makes  great  demands  upon 
the  professional  statistician  is  due  partly  to  the  necessity 
of  completely  comprehending  the  purpose  of  practical 
problems  arising  in  the  most  varied  fields  of  political 
and  economic  life  and  scientific  research,  in  order  to  make 
them  susceptible  to  statistical  treatment.  Everything  to 
be  considered  must  either  directly  or  by  symptoms  assume 
the  form  of  things  capable  of  enumeration,  possibly  of  such 
as  have  qualities  which  can  be  measured.  The  indefinite 
ideas  and  conjectures  from  examples,  which  fill  our  ordinary 
thought,  can  never  take  the  place  of  the  complete  obser- 
vation with  its  numerical  results.  To  determine  what 
is 


214  Annals  of  the  American  Academy. 

aggregates  may  be  considered  analogous  and  compared, 
and  whether  their  enumerations  are  of  value,  requires  sharp 
discrimination  and  often  comprehensive  knowledge  and 
research.  Causality  and  probability  cannot  always  be 
ascertained  without  a  profound  penetration  into  actual 
and  historical  premises  and  conditions. 

But  the  real  difficulties  are  not  to  be  found  here.  On 
the  contrary,  these  demands  when  they  arise  only  stimu- 
late and  interest.  The  chief  requirement  is  to  keep  up 
the  interest,  the  continued  tension,  which  enables  the  sta- 
tistician to  handle  each  of  these  endless  repetitions  of  the 
same  ideas  and  totals  with  the  same  energy.  There  are 
no  means  of  attaining  this  except  the  change  of  the  de- 
mands and  the  increase  of  responsibility  for  their  fulfilment. 
The  tedium  of  monotony  and  the  consciousness  of  not 
making  personally  the  finishing  touches,  are  the  greatest 
enemies  of  good  achievements  and  capacity. 

It  is  therefore  highly  desirable  to  make  the  specialist  as 
far  as  possible  head  of  the  statistics  for  a  certain  district, 
so  that  he,  himself,  with  not  more  than  one  scientific  as- 
sistant, can  attend  to  all  special  matters  which  cannot  be 
considered  merely  mechanical,  and  hence  all  the  problems 
engage  his  attention  in  comparatively  rapid  variation,  and 
lead  him  to  the  desire  and  necessity  of  carrying  on  these 
works  originally,  intensively,  and  definitely. 

The  organization  of  bureaus  for  smaller  districts  is  to 
be  preferred  to  the  establishment  of  a  single  centralized 
institution  for  other  reasons.  From  the  centre  of  a  small 
State  or  a  province  or  a  district  there  remains  a  possibility 
of  that  local  and  personal  knowledge  which  is  of  the 
utmost  importance  for  estimating  the  value  of  different 
organs  and  their  mode  of  procedure,  for  detecting  errors, 
and  for  ascertaining  the  reliability  of  the  conclusions 
drawn.  The  examination  of  the  returns  is  also  essentially 
facilitated.  They  are  not  in  such  an  enormous  number  as 
to  escape  the  supervision  of  the  director,  and  they  do  not 
come  from  places  and  conditions  so  distant  and  different 


Theory  and  Technique  of  Statistics.  215 

that  mistakes  cannot  be  much  more  easily  detected,  and 
corrections  much  more  easily  undertaken  with  promise  of 
better  results. 

Such  a  small  bureau  can  give  assistance  and  instructions 
within  its  district  in  a  way  impossible  to  a  large  central 
institution.  The  local  officials  can  apply  directly  to  it  for 
explanations,  which  it  would  be  difficult  to  obtain  from 
the  general  publications.  The  small  bureau  can  also  apply 
itself  to  problems  of  local  importance  which  a  central  bu- 
reau could  not  properly  supervise,  though  it  should  under- 
take them.  (v.  Scheel  (§  1 1 3),  Zeitschrift  f.  d.  gesammt. 
Staatswissenchaft,  1869,  1  Heft.) 

The  cost  of  statistics  is  in  no  sense  greater  for  decen- 
tralized than  centralized  organization,  since  the  same  labor 
is  to  be  accomplished.  At  the  introduction  of  the  modern 
card  system  it  was  supposed  that  it  would  be  cheaper  in 
large  factories.  But  this  was  only  until  its  conditions  had 
been  learned  by  trial.  When  all  the  steps  and  all  the 
accessories  of  the  work  are  fully  known,  when  uniform 
instructions  and  schedules  have  been  distributed  to  the 
smaller  bureaus,  we  must  consider  their  less  expensive 
office  rent  and  salaries,  the  immediate  supervision  of  the 
director,  as  well  as  the  greater  demands  which  a  centralized 
organization  makes  upon  the  general  administration. 

There  must  of  course  be  a  central  institution  superior  to 
the  local  bureaus.  It  provides  the  uniform  plan  and  for 
the  uniformity  and  collation  of  results.  In  §  50  attention 
has  already  been  called  to  the  benefits  which  have  resulted 
from  the  position  of  the  German  Statistical  office  as  erected 
by  the  resolutions  of  the  Bundesrath,  as  compared  with  the 
numerous  statistical  bureaus  of  the  single  States,  chiefly  in 
promoting  the  method.  But  it  would  not  do  to  conclude 
from  the  recognized  superiority  of  the  growing  labors  of 
this  bureau  peculiar  advantages  in  centralization.  This 
would  overlook,  on  the  one  hand,  that  the  German  Empire 
was  so  fortunate  as  to  possess  in  the  first  director  of  sta- 
tistics a  man  of  extraordinary  critical  endurance  and  acute- 


216  Annals  of  the  American  Academy. 

ness,  and  of  remarkable  clearheadedness  in  the  conception 
of  the  technical  requirements  of  the  work ;  and  it  would 
overlook,  upon  the  other  hand,  that  the  most  admirable 
achievements  of  a  centralized  institution  cannot  make  up 
for  the  loss  of  those  advantages  which  the  lack  of  smaller 
bureaus  necessarily  entails. 

§117.     THE   POSITION   OF   STATISTICS   IN    GENERAL    CULTURE. 

The  means  of  promoting  the  proper  appreciation  and 
use  of  statistics,  outside  of  statistical  bureaus,  must,  as  a 
matter  of  course,  consist  in  spreading  correct  knowledge, 
and  in  the  increase  of  the  number  of  those  who  have  been 
instructed  in  theoretical  statistics. 

In  this  connection  it  is  highly  desirable  to  have  a  certain 
number  of  young  administrative  officials  pass  as  assistants 
through  the  statistical  bureaus.  This  would  involve  con- 
siderable inconvenience  for  the  director,  for  he  would  have 
to  instruct  them,  and  it  would  require  some  time  before 
they  could  furnish  sufficiently  useful  and  reliable  work. 
Their  occupation  could  not  therefore  be  calculated  for  a 
very  short  period,  but  should  be  placed  at  from  four  to 
five  years.  It  could,  however,  be  counted  to  their  credit, 
like  any  other  administrative  work,  for  they  would  receive 
great  benefit  from  it,  and  take  with  them  a  knowledge  and 
experience  and  a  critical  insight  into  statements  of  fact, 
which  would  be  of  service  in  any  office  to  which  they 
might  be  assigned,  and  promote  generally  the  proper 
comprehension  of  statistics. 

Such  an  arrangement  would  aid  in  discovering  the  per- 
sons, who  are  by  no  means  numerous,  especially  qualified 
for  statistical  work,  and  thus  variety  in  the  labors  of  the 
directors  of  statistical  institutions  could  be  more  easily 
introduced. 

For  such  preparation  statistical  seminaries  have  been 
created.  One  was  established  by  a  Ministerial  Rescript 
of  August  18, 1862  (Preuss.  Minist.  Blatt.  f.  d.  innere  Verw., 


Theory  and  Technique  of  Statistics.  217 

1862,  p.  257),  in  connection  with  the  Prussian  Statistical 
Bureau.  Other  seminaries  have  been  established  by  pro- 
fessors of  political  science  at  universities,  such  as  Halle, 
Leipzig,  and  Strassburg.  It  is  important  whether  such 
institutions  are  conducted  with  the  intention  of  schooling 
statistical  specialists  or  for  the  instruction  of  students.  The 
first  requires,  besides  the  usual  scientific  preparation,  ex- 
tensive practice  from  occupation  with  the  first  material  to 
the  conception  of  definite  problems.  It  is  presumably  to 
be  attained  best  when  it  is  looked  upon  as  a  profession, 
and  gained  by  work  as  a  clerk  and  then  as  assistant  in  a 
bureau. 

For  the  purpose  of  instructing  students  of  political 
economy  and  others  who  are  not  looking  forward  to  a 
statistical  career,  the  seminar  cannot  attempt  extensive 
undertakings  which  would  occupy  the  student  for  some 
time,  and  thus  draw  his  attention  from  his  studies.  Such 
seminars  are  limited  to  smaller  essays,  usually  to  discus- 
sion of  examples  and  demonstrations.  Nevertheless  it  is 
just  as  fruitful  for  theoretical  education  as  it  is  indispens- 
able. It  differs  chiefly  from  the  statistical  exercises  which 
form  the  practical  part  of  the  lectures  only  by  certain 
appliances,  such  as  a  regularly  accessible  library,  working- 
rooms,  collection  of  schedules,  diagrams,  means  for  calcula- 
tion and  drawing,  and  the  like,  which  are  very  desirable. 

Yet  the  question  of  the  preparation  of  specialists  is  by 
no  means  the  all-absorbing  topic.  The  demand  for  them 
is  not  so  great  but  that  a  substitute  may  be  found.  This 
will  be  all  the  more  easy  if  the  effort  to  bring  into  the 
general  culture  a  clearer  conception  and  comprehension 
of  statistics,  which  stands  obviously  in  the  foreground,  is 
successful. 

In  this  effort  the  burden  of  the  task  falls  upon  the  uni- 
versities. It  is  important  to  spread  as  far  as  possible  the 
theory  of  statistics,  for  theoretical  education  does  not 
mean  anything  else  than  gaining  knowledge  from  sys- 
tematically arranged  principles  and  illustrations,  in  con- 


2i 8  Annals  of  the  American  Academy. 

trast  to  the  experience  gained  by  a  practice  of  the  art. 
For  it  is  evident  that  the  numerical  results  of  statistics 
without  reference  to  the  fields  of  knowledge  which  they 
serve — geography,  anthropology,  political  economy,  his- 
tory, etc. — cannot  be  subjects  of  instruction  except  as 
examples  of  method  and  of  its  possible  results.  The 
method  itself  can,  however,  be  presented  as  a  connected 
body  of  thought. 

It  is  indeed  a  body  of  doctrine  preeminently  adapted  as 
preparation  and  support  of  a  general  scientific  education. 
It  is  closely  united  to  the  first  bases  of  human  percep- 
tion and  logical  thought,  and,  unlike  theoretical  logic, 
does  not  develop  from  these  ideas  an  apparently  abstract 
and  abstruse  system  of  syllogisms,  but  shows  directly  and 
clearly  how  these  logical  connections  are  turned  to  account 
in  problems  of  economic  and  political  life,  of  a  thoroughly 
practical  and  indispensable  character.  In  every  new  ex- 
planation it  shows  in  a  new  form  how  the  slightest  error 
of  an  idea  or  smallest  logical  mistake  can  render  large 
undertakings  useless,  and  in  their  consequences  mislead- 
ing and  even  dangerous  for  the  judgment  of  important 
facts  of  political  and  social  existence. 

The  theory  of  statistics  shows  also  the  value  and  appli- 
cation of  logic,  and  must  heighten  the  interest  in  critical 
thought.  It  leads  to  a  comprehension  of  the  earnest  and 
firm  purpose  of  statistical  endeavor,  to  a  consciousness  that 
requires  strict  truth  and  love  of  the  truth,  that  the  proper 
treatment  of  the  conclusions  or  data,  which  will  not  permit 
or  excuse  any  self-deception,  involves  a  serious  responsi- 
bility, that  may  properly  be  designated  as  a  demand  of  the 
public  conscience. 

For  the  youth  of  all  professions,  particularly  those  of 
official  position,  the  theory  of  statistics  is  a  very  appro- 
priate field  of  study.  When  its  way  is  opened  more  and 
more  among  students  we  may  expect  a  reaction  upon 
political  bodies,  the  press,  public  opinion,  and  general 
culture.     We  shall  then  become  accustomed  to  a  more 


Theory  and  Technique  of  Statistics.  210 

critical  treatment  of  statistical  questions;  ambiguities  of 
conception,  of  interpretation,  and  proposals  will  decrease; 
statistics  will  be  more  exactly  applied  in  their  true  fields, 
and,  with  proofs  of  their  value,  the  general  estimate  of 
them  will  be  higher. 


y* 


Note.  Appendices  III.,  IV.,  and  VI.  are  placed  opposite 
the  paragraphs  to  which  they  refer,  in  order  to  facilitate 
comparison  with  the  text. 


APPENDIX. 


Appendix  I.  (to  \  14)  Halley's  Tables  of  Mortality. 

Halley's  Report — An  Estimate  of  the  Degrees  of  the  Mortality  of 
Mankind,  Drawn  from  Curious  Tables  of  the  Births  and  Funerals  of 
the  City  of  Breslau,  with  an  Attempt  to  Ascertain  the  Price  of  Annui- 
ties upon  Lives  (Philosophical  Transactions,  Vol.  XVII.,  for  the  year 
1693,  15  pp.  in  No.  196,  and  3  pp.  in  No.  198) — says  that  in  the  tables 
under  consideration  for  the  five  years  1687  to  1691,  the  age  and  sex 
of  all  who  died  in  the  city  of  Breslau  is  registered  with  all  possible 
care  and  exactness,  and  that  the  figures  are  given  by  months  and 
compared  with  the  births.  Complete  materials  for  the  year  1691  were 
also  preserved.  It  would  appear,  however,  that  Halley's  observations 
are  based  mainly  on  the  following  table,  which,  as  the  main  result  of 
Neumann's  work,  had  been  transmitted  to  him  with  the  other  papers. 
The  upper  line  gives  the  age,  and  the  one  just  below  the  number  of 
persons  of  that  age  who  died  in  each  year.  Where  no  number  is 
given  in  the  upper  line  the  lower  figure  indicates  the  number  of  per- 
sons who  died  each  year  in  the  period  between  the  previous  and  suc- 
ceeding ages : 

7       8       9       .      14        .        18  .         21  .      27      28        .       35 

*    "H  "       "        6      5i      2        3J        5  6  4$        6\      9        877 


36    .   42   .   45    •    49   "•  I  54 
8    9i   8   9    7    7    10   LiojJ  11 

55   56    .63 
9    9   10   12   9$ 

70   71   72   .   77    .    81     .    84 
14    9   11   9i   6    7    3    4     2 

.   90   91  r.i  98 
1     1     1   LiJ    ° 

99  IOO 

\  \ 

The  two  points  in  brackets  are  not  to  be  found  in  the  essay,  but 
this  must  be  a  printer's  error,  for,  as  Knapp  has  pointed  out,  they 
must  be  supplied.    (Theorie  des  Bevolkerungswechsels,  1874,  p.  125.) 

(221) 


222  Annals  of  the  American  Academy. 

Halley  has,  as  shown  in  his  calculations,  supplemented  this  table  with 
other  observations,  so  as  to  secure  a  regular  progression,  which  might 
serve  as  a  general  scale,  as  follows : 


7 

• 

9 

• 

14 

. 

18 

. 

21 

• 

27 

28 

. 

35 

12 

10 

9 

6| 

6 

6 

6 

6 

6 

6f 

7 

7 

8J 

9 

36 

42 

45 

. 

49 

54 

. 

56 

63 

9 

9 

10 

10 

10 

10 

11 

11 

10 

10 

10 

10 

10 

10 

70 

. 

72 

77 

81 

84 

N 

11 

11 

11 

ioi 

10 

8 

6 

4 

2 

UJ 

The  principal  change  is  in  the  number  of  deaths  between  the  9th  and 
1 8th  years.  He  increased  this,  as  he  held  the  small  number  in  the 
table  to  be  merely  accidental.  He  was  correct  in  this,  but  went  too 
high  on  his  part. 

Halley  says  that  it  appears  from  the  Breslau  tables  that  in  the  years 
in  question  there  were  6198  births  and  5896  deaths  (1 173^  yearly,  there- 
fore). Hence  the  growth  of  the  population  is  about  64  in  each  year,  or 
about  one-twentieth,  but  this  is  probably  equalized  by  recruiting  for 
the  Imperial  military  service.  But  as  this  is  problematical,  the  num- 
ber of  births,  however,  well  known,  it  may  be  supposed  that  the  popu- 
lation of  Breslau  grows  by  1238  births  annually.  It  appears  further, 
from  the  same  tables,  that  on  an  average  348  die  in  the  first  year  of 
their  age ;  that  only  890  reach  the  age  of  1  year ;  that  between  the 
completion  of  the  1st  and  that  of  the  6th  year,  198  die  on  the  aver- 
age, and  hence  only  692  survive  the  sixth  year. 

On  this  basis  he  constructed  the  following  table.  This,  he  says, 
shows  the  number  of  the  population  of  Breslau  in  all  ages  from  birth 
to  old  age,  and  shows,  therefore,  the  probability  of  death  at  each  age. 
This  shows  how  annuities  may  be  calculated,  which  until  then  had 
only  an  imaginary  basis,  and  also  shows  what  are  the  chances  that  a 
person  of  one  age  should  reach  some  more  advanced  age.  In  his 
language,  "this  table  does  show  the  number  of  persons  at  the  age 
current  annexed  thereto,  as  follows :" 


Theory  and  Technique  of  Statistics. 


223 


Age 
cur- 
rent 

Per- 
sons. 

Age 
cur- 
rent. 

Per- 
sons. 

Age 
cur- 
rent. 

Per- 
sons. 

Age 
cur- 
rent. 

Per- 
sons. 

Age 
cur- 
rent. 

Per- 
sons. 

Age 
cur- 
rent. 

Per- 
sons. 

I 
2 

3 
4 
5 
6 

7 

IOOO 

855 
798 
760 
732 
710 
692 

8 

9 
IO 
II 

12 
13 

14 

680 
670 
661 

653 
646 
640 
634 

15 
16 

17 
18 

19 
20 
21 

628 
622 
616 
6lO 
604 
598 
592 

22 
23 
24 
25 
26 

27 
28 

586 
579 
573 
567 
560 

553 
546 

29 

30 
31 
32 
33 
34 
35 

539 
531 

523 
515 
507 
499 
490 

36 
37 
38 
39 
40 

41 
42 

481 
472 
463 
454 
445 
436 
427 

43 

417 

5o 

346 

57 

272 

64 

202 

7i 

131 

78 

58 

44 

407 

5i 

335 

58 

262 

65 

192 

72 

120 

79 

49 

45 

397 

52 

324 

59 

252 

66 

182 

73 

109 

8p 

4i 

46 

387 

53 

3i3 

60 

242 

67 

172 

74 

98 

81 

34 

47 

377 

54 

302 

61 

232 

68 

162 

75 

88 

82 

28 

48 

367 

55 

292 

62 

222 

69 

152 

76 

78 

83 

23 

49 

357 

56 

282 

63 

212 

70 

142 

77 

68 

84 

20 

Age. 

I 
14 

21 

28 

35 
42 
49 
56 


Persons. 
5,547 
4.584 
4,270 

3.964 
3.604 
3,178 
2,709 
2,194 


Age. 
63 
70 

77 

84 

100 


Total 


Persons. 

1,694 

1,204 

692 

253 
107 

34,000 


The  first  series  shows  how  many  of  1238  persons  born  in  Breslau 
die  in  each  age  class.  The  second  series  shows  a  general  order  of 
mortality,  as  Halley  called  it,  based  on  the  former. 

If  to  explain  the  two  series  we  assume  that  the  1000  persons  noted 
by  Halley  in  the  age  current  1  represent  the  births  of  the  1st  year, 
then  the  entire  calculation  must  be  reduced  to  1000  instead  of  1238, 
and  this  reduction  must  appear  in  the  further  figures.  But,  since  for 
1238  persons  born,  890  are  said  to  survive  the  1st  and  692  the  6th  year, 
the  number  at  the  age  current  2  must  be  not  855,  but  719,  and  hence 
all  the  following  figures  must  be  too  high.  Hence  the  population  of 
Breslau  could  not  be  counted,  as  is  done  above  in  the  second  series, 
by  adding  together  the  first.  If,  on  the  other  hand,  it  should  be  sup- 
posed that  the  number  of  persons  opposite  each  age  current  repre- 
sented the  average  number  of  persons  living  in  each  year,  it  would 
be  seen  that  1000  instead  of  1238  was  not  appropriate  in  view  of  the 
greater  mortality  of  the  early  months.  Hence  it  would  be  seen  that, 
though  the  following  numbers  might  be  averages,  it  would  not  agree 


224  Annals  of  the  American  Academy. 

with  Halley's  statement,  that  692  survive  the  6th  year,  to  find  the  same 
figures  in  the  middle  of  the  7th  year.  All  subsequent  figures  would, 
therefore,  disagree. 

If  the  figures  opposite  each  age  current  are  not  those  living  at  the 
beginning  of  the  year  or  at  the  middle  of  it,  they  can  only  represent 
those  who  survive  each  age.  This  agrees  with  the  supposition  that  of 
1238  persons  born  692  survive  the  6th  year  to  find  this  figure  opposite 
the  age  current  7.  Hence,  working  backwards,  we  find  surviving  the 
5th  year  710;  the  4th,  732  ;  the  3d,  760 ;  the  2d,  798,  and  the  1st  855. 
On  the  other  hand,  Halley  gives  this  last  at  890,  and  the  number  1000 
could  only  be  the  average  number  during  the  first  year. 

Although  Halley  laid  no  great  weight  on  these  calculations  of  esti- 
mates, we  have  still  no  ground  to  suppose  that  he  made  any  mistakes 
in  his  figuring,  and  the  difficulties  in  his  niethods  cannot  be  solved 
with  such  material  as  has  been  preserved. 

(G.  F.  Knapp:  Theorie  des  Bevolkerungswechsels,  1874. 

J.  Graetzer:  Edmund  Halley  und  Caspar  Neumann,  Breslau,  1883. 

E.  Rehnisch :  Review  of  the  last  work  in  Gottinger  Gelehrten  An- 
zeigen,  1883,  p.  1576.) 


Theory  and  Technique  of  Statistics.  225 


Appendix  II.  (to  $  48)  System  of  Resolutions   of  the  Inter- 
national Statistical  Congress.    (Compte-rendu 
general,  St.  Petersburg,  1872.) 

A.  THEORETICAL  AND  GENERAL  STATISTICS. 

1.  Theory  and  Technique  of  Statistics, 

General  treatment  of  methods. 
Graphical  methods  and  cartography. 
Uniformity  of  terminology. 
Statistical  instruction. 

2.  Statistical  Organization. 

General  principles  of  organization ;  central  commissions ;  scope 

of  statistical  organs. 
Statistical  publications. 
Exchange  of  the  same. 

3.  Organization  of  the  Congress. 

Resolutions  on  organization,  statutes,  and  work  of  later  Con- 
gresses (temporary  regulations). 
Plan  for  comparative  international  statistics. 

B.   PRACTICAL  OR  SPECIAL  STATISTICS. 

1.  Territory  and  Nature  of  the  Country, 

Cartography  in  relation  to  catasters  and  the  transfer  of  property. 

Hydrography. 

Application  of  natural  sciences  to  statistics. 

Meteorology. 

2.  Place  of  Residence. 

Statistics  of  large  cities.  v 

3.  Population. 

Census :  data  to  be  collected,  methods  of  enumeration. 
Subsidiary  questions  to  enumeration  of  population,  necessary  for 

a  general  view  of  the  nation. 
Population  registers. 
Movement  of  the  population. 
Death  tables. 
Emigration. 
Basis  of  ethnographic  statistics. 

4.  Health  and  Sickness. 

Statistics  of  geographical  influences  on  health. 
Statistics  of  deaths. 
Statistics  of  epidemics. 


226  Annals  of  the  American  Academy. 

Statistics  of  mental  diseases. 

Statistics  of  institutions  for  the  sick. 

Military  medical  statistics. 

Comparative  statistics  of  health  and  mortality  of  the  civil  and 

military  population. 
Statistics  of  accidents  in  transportation,   factories,  mines,  and 

furnaces. 

5.  Real  Property. 

General  resolutions,  division,  and  extent  of  property  in  land. 

Modes  of  ownership. 

Transfer  of  ownership,  prices,  and  indebtedness. 

Catasters. 

Buildings. 

6.  Agriculture  and  Grazing. 

Agricultural  investigations,  data  to  be  collected,  and  methods  to 
be  pursued. 

7.  Fisheries. 

Statistics  of  fisheries. 

8.  Mines  and  Furnaces. 

General  resolutions. 

9.  Industry. 

General  statistics  of  labor. 
Special  statistics  of  industries. 

10.  Production  and  Consumption. 
General  resolutions. 

11.  Laboring  Classes,  Prices,  Wages, 
General  resolutions. 

Budgets  of  the  laboring  classes. 
Prices  and  wages. 

12.  Public  Charity. 

Resolutiors  on  statistics  of  the  systems  and  arrangements  for 
public  charity. 

13.  Money,  Weights,  and  Measures. 
Uniformity  of  money,  weights,  and  measures. 

14.  Commerce. 
General  resolutions. 
Foreign  commerce. 

15.  Transportation,  Shipping. 
Statistics  of  country  roads. 
Statistics  of  railroads. 
Statistics  of  inland  navigation. 
Statistics  of  maritime  navigation. 
Statistics  of  postal  service. 
Statistics  of  telegraphs. 


Theory  and  Technique  of  Statistics.  227 

16.  Banks  and  Institutions  of  Credit. 

Statistics  of  stock  corporations. 

Statistics  of  banks. 

Land  credit. 

Circulation  of  bank  notes  and  paper  money. 

17.  Insurance. 

Resolutions  on  the  statistics  of  insurance. 

18.  Charity  and  Care  of  the  Poor. 

Statistics  of  the  poor.  « 

Dependent  persons. 

19.  Public  Education ,  Art,  and  Science. 
Schools  and  public  education. 
Institutions  for  instruction  in  the  fine  arts. 
Institutions  for  the  preservation  of  scientific  collections. 
Institutions  for  the  preservation  of  collections  of  the  fine  arts. 

20.  Justice. 

General  resolutions,  judiciary  organization. 

Statistics  of  criminal  courts. 

Statistics  of  civil  and  commercial  causes. 

21.  Prisons  and  Police. 

Statistics  of  prisons. 

22.  Army  and  Navy. 

General  statistics  of  land  and  naval  forces. 
Special  statistics  of  marines. 
Medical  statistics  of  army  and  navy. 

23.  Finance. 

General  statistics  of  finance. 

Yearly  income  of  the  nation. 

Statistics  of  expenditure. 

Finances  of  cities,  the  church,  corporations. 

24.  Statistics  of  Municipalities. 
General  resolutions. 

25.  Statistics  of  Colonies. 
General  resolutions. 


Appendix  V.  (to  §ioo)  Enumeration  Card  for  Additions. 


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Theory  and  Technique  of  Statistics.  229 


REMARKS 


1.  For  each  election  district  in  which  the  candidate  was  elected  in  the  first 

election,  a  white  card  is  to  be  used.  For  first  elections  which  were 
not  decisive,  a  yellow  card  is  to  be  used.  For  the  decisive  after 
elections,  a  blue  card  is  to  be  used. 

After  elections  which  are  not  decisive  are  not  considered. 

The  party  of  the  successful  candidate,  or  the  plurality  candidate,  is  to  be 
underlined  with  red,  that  of  the  principal  opposing  candidate  with 
blue.     In  addition,  this  must  be  written  out  as  required  by  the  blank. 

2.  The  votes  are  to  be  counted  by  parties,  whether  given  to  one  or  to  several 

candidates. 

3.  For  the  answers  to  the  questions  as  to  the  geographical  position,  urban  or 

rural  population,  as  well  as  prevailing  religion,  a  special  list  is  given, 
from  which  they  can  be  obtained. 


This  card  is  not  filled  out  in  the  election  district,  but  in  the  statistical 
bureau  from  the  election  returns.  The  contents  between  the  columns  b  and 
c  can  be  treated  like  the  ordinary  card  to  obtain  results  by  sorting  as  shown  in 
Appendix  IV. 

In  the  columns  a  and  c,  on  the  other  hand,  totals  are  entered  by  units,  tens, 
hundreds,  etc.,  in  exactly  the  same  way  on  each  card.  They  can  be  placed, 
therefore,  one  over  the  other  and  these  totals  added  without  further  transcribing. 

The  column  b  contains  percentage  calculations,  but  if  it  contained  totals  they 
could  be  used  for  addition,  after  the  column  a  was  completed,  by  cutting  off 
or  folding  over  this  column. 


230  Annals  of  the  American  Academy. 


Appendix  VII.  (§  93)  The  Calculation  of  Mortality  Tables. 

The  calculation  of  a  table  of  mortality  or  survival  is  the  solution  of 
the  problem  of  finding  how  many  persons,  in  a  given  district  and 
period,  who  were  born  in  the  same  year  will  survive  in  each  succeed- 
ing year.  The  proof  may  be  based  on  the  gradual  diminution  by 
death  of  an  actual  or  ideal  generation. 

An  actual  generation  would  include  all  persons  born  in  the  given 
district,  in  the  given  period  of  one  or  several  years,  from  the  time  of 
birth  until  the  expiration  of  the  last  person.  In  an  imaginary  gener- 
ation, on  the  other  hand,  the  total  number  of  persons  living  and  dying 
in  the  district  for  the  period  in  question  are  so  united  that  the  propor- 
tion of  persons  of  each  age  who  die  to  the  persons  alive  at  that  age, 
gives  the  picture  of  the  life  and  death  of  an  actual  generation. 

The  first  method  dates  from  Herrmann  (g  44),  and  has  also  been 
attempted  in  Baden,  Prussia,  and  Cisleithania.  It  has  been  shown  to 
be  impracticable,  on  account  of  the  need  of  maintaining  the  observa- 
tion 100  years  and  the  changes  in  the  population  through  emigration. 
The  second  method  is  generally  in  use  and  satisfies  the  main  purpose 
of  the  question ;  that  is,  to  find  the  present  mortality  at  different  ages. 
Its  proper  conception  and  application  is  very  complicated.  It  is  ren- 
dered especially  difficult  by  the  fact  that  it  is  necessary  to  compare 
the  living  population,  as  ascertained  on  a  given  day,  with  the  deaths 
for  a  whole  year,  and  yet  preserve  the  equality  in  the  ages.  The  dis- 
cussion of  this  condition  of  the  problem  is  found  as  early  as  War- 
gentin.  It  has  probably  been  stated  by  none  so  clearly  and  instruc- 
tively as  by  K.  Becker. 

K.  Becker  has  discussed  the  theory  in  detail.  (Anhang  zum,  r.  Theil 
des  IXten  Heftes  der  Statistischen  Nachrichten  iiber  das  Grossherzog- 
thum  Oldenburg.)  But  the  shortest  and  simplest  statement  is  to  be 
found  in  a  rather  obscure  place  (Stat.  d.  D.  R.,  Vol.  XX.  p.  145, 
Bericht  iiber  die  Reichs-Medizinalstatistik,  vom  7.  Oktober,  1874). 
Here  he  says : 

"  To  find  a  sufficient  expression  for  mortality,  we  must  be  able  to 
ascertain  it  for  distinct  age  periods,  and,  if  we  would  be  in  any  way 
exact,  for  each  year  of  life.  This  is  the  necessary  basis  for  any  further 
consideration  of  mortality.  As  a  matter  of  course  we  must  know  the 
ages  of  the  dying.  But  this  alone  is  not  sufficient.  On  the  contrary, 
it  is  essential  to  know  the  year  of  birth  of  those  who  die.  This  is 
shown  by  the  following  illustration  : 

"  Suppose  we  are  to  find  the  mortality  in  the  first  year ;  that  is, 
show  how  many  of  a  number  of  persons  born  die  before  completing 
their  first  year.     These  data  are  given : 


Theory  and  Technique  of  Statistics.  231 

Born  in  1861 7218 

Deaths  of  persons  from  0-1  year  of  age  in  1861  .  .  936 
Deaths  of  persons  from  0-1  year  of  age  in  1862  .  .  848 
"How  shall  we  make  our  calculations?  We  cannot  compare 
the  births  of  the  year  1861  with  the  deaths  of  persons  from  0-1 
year  of  age  in  1861,  since  the  latter  were  manifestly  not  all 
born  in  1861,  but  partly  in  i860.  Just  as  little  may  we  prop- 
erly compare  the  births  of  1861  with  the  deaths,  as  given  above, 
for  1862,  since  the  latter  include  children  who  were  born  in  1862. 
To  solve  the  problem  of  finding  how  many  of  the  children  born 
in  1 861  died  in  their  first  year  we  must  take  our  recourse  to  a 
hypothesis,  either  that  the  deaths  of  the  year  1861  or  of  1862  all  come 
from  the  births  of  1 861,  or  that  of  the  deaths  of  1861  one-half  were 
from  births  of  i860  and  one-half  from  those  of  1861,  and  in  the  same 
way  that  half  of  the  deaths  of  1862  were  from  1861  and  half  from  1862 
— mere  hypotheses  that  may  be  in  glaring  contradiction  with  the  facts. 
"The  proof  is  quite  as  incomplete  if  the  persons  dying  are  sepa- 
rated not  by  age,  but  by  the  year  of  birth,  as  when  we  have  the  fol- 
lowing data : 

Births  of  the  year  1 861 7218 

Deaths  of  persons  born  in  1861 : 

Diedini86i 647 

Died  in  1862 387 

"  Here  we  know,  indeed,  that  the  last-named  persons  were  born  in 
1861,  but  the  647  who  died  in  the  year  1861  form  only  a  portion  of 
the  persons  born  in  1861  who  died  in  their  first  year.  The  remainder 
are  to  be  found  among  the  387  who  died  in  the  year  1862,  some  of 
whom,  however,  must  have  been  within  their  second  year.  Again, 
we  must  have  recourse  to  a  doubtful  hypothesis. 

"  A  second  illustration  may  be  taken  from  a  more  advanced  period 
of  life.    Suppose  we  are  to  ascertain  the  mortality  in  the  63d  year 
(z.  e„  of  persons  from  62  to  63  years  of  age),  in  other  words,  to  find 
how  many  persons  who  reached  the  age  of  62   died  before  they 
became  63  years  of  age.    We  have  the  following  data  : 
Population  at  the  close  of  the  year  1861,  at  the  age  of  62 
to  63  years,  or,  what  is  the  same  thing,  population 
born  in  1799  living  at  the  close  of  the  year  1861       .     1598  (A.) 
In  the  first  case  the  deaths  by  ages. 
Deaths  at  the  age  of  62  to  63  years : 

Diedini86i 73  (B.) 

Died  in  1862         .         .  v 71 

In  the  second  case  deaths  by  year  of  birth : 
Deaths  of  persons  born  in  1799  : 

Diedini86i 59(C) 

Died  in  1862 84 


232  Annals  of  the  American  Academy. 

"  Neither  in  the  first  or  second  case  can  we  ascertain  the  number  of 
persons  who  became  62  years  of  age  and  the  number  of  those  who 
died  before  the  age  of  63.  The  persons  who  became  62  years  of  age 
in  the  course  of  1861  consist  of: 

"  (a)  Those  at  the  age  of  62  to  63  years  at  the  close  of  1861,  or  those 
born  in  1799  (See  A.  above). 

"(b)  Those  at  the  age  of  62  to  63  years  who  died  during  1861, 
and  who  became  62  years  of  age  in  1861  (not  in  i860),  or,  in  other 
words,  who  were  born  in  1799.  This  number  cannot  be  found  from 
the  figures  given  above,  since  the  number  (B.)  includes  persons  born 
in  1798,  and  (C.)  persons  who  died  at  the  age  of  61  to  62  years. 

"  The  persons  who  became  62  years  of  age  in  1861,  and  died  before 
reaching  63  years,  consist  of  the  persons  of  62  to  63  years  of  age  who 
died  in  both  years  1861  and  1862,  and  who  were  born  in  1799.  This 
number  cannot  be  found  from  the  data  given  any  more  than  that 
marked  (b)  above. 

"  Therefore,  we  must  again,  as  in  the  first  illustration,  have  recourse 
to  hypotheses  that  are  very  unreliable,  and  cannot  promise  safe 
results. 

"  This  can  be  avoided  only  when  we  have  the  facts  not  only  for  the 
age  of  those  who  die,  or  the  year  of  birth,  but  for  both  of  these.  Then 
the  calculations  may  be  made  in  the  following  fashion : 

FIRST   ILLUSTRATION. 

Births  of  the  year  1861 7218 

Died  at  the  age  of  0-1  year : 

f  Born  in  i860       ......  286 

In  1861  J  Born  in  Ig6l        ......  647 

)  Born  in  1861 239 

Inl862|  Born  in  1862 609 

"Accordingly,  of  7218  persons  born  in  1861,  647  +  239  =  886  died 

QQfi 

in  the  first  year.    The  mortality  is,  therefore,  -.   100  =12.27  per 

721b 

cent.,  or  the  probability  of  death  in  the  first  year  =  o.  1227. 

SECOND  ILLUSTRATION. 

Population  at  the  close  of  the  year  1 861  at  the  age  of 
62-63  years 1598 

Died  at  the  age  of  62-63  years  : 

f  Born  in  1798 33 

In  l861  1  Born  in  1799 40 

Inl862l  Born  in  1800 39 


Theory  and  Technique  of  Statistics.  233 

"Accordingly,  in  the  course  of  the  year  1861,  1598  +  40=  1638  per- 
sons became  62  years  of  age.  Of  these  40  +  32  =  72  died  before  reach- 
ing 63  years  of  age.    The  mortality  is,  therefore,  -L-. . .  100  =  4.39  per 

cent.,  or  the  probability  for  62-year-old  persons  of  death  in  the  63d 
year,  0.0439." 

In  this  way  the  probability  of  death  (w)  is  calculated  for  persons  at 
each  age,  and  correspondingly  the  probability  of  life  (1 — w). 

Let  us  assume  that  the  probability  of  death  has  been  calcu- 
lated in  this  way  on  the  basis  of  the  Mortality  Table  for  Prussia, 
published  by  R.  Boeckh  in  Hildebrand's  Jahrbuchern,  Vol.  XXV., 
Nos.  4-5,  with  valuable  explanations.  This  probability  is  for  all  males 
born  (including  still-born)  in  the  year  1864  whose  ages  range  from  o 
to  possibly  1  year ;  i.  e. ,  therefore, 

For  all  at  the  age  0-1  year 0.27058 

"     "    "    "     "     1-2  years 0.09070 

2-3     " 0.04942 

3-4    " 0.02832 


<<    <«    <<     (i 
<(    <(    <<     (< 


According  to  this  ratio  of  100,000  persons  born  (including  still- 
born)— 

There  died  at  the  age  of  0-1  year      ....    27,058 

Hence  there  survived  the  first  year    ....    72,942 
Of  these  the  following  died  at  the  age  or  1-2  years  .      6,616 

Hence  there  survived  the  second  year       .        .        .66,326 
Of  these  the  following  died  at  the  age  of  2-3  years  .      3,278 

Hence  there  survived  the  third  year  ....    63,048 
Of  these  the  following  died  at  the  age  of  3-4  years  .       1,783 

Hence  there  survived  the  fourth  year       .         .        .     61,265 
And  so  forth,  as  in  column  7  of  the  table. 

Carried  through  all  the  ages  this  calculation  shows  how  many  of 
the  100,000  born  die  at  each  age  and  how  many  survive  it. 

If  we  wish  the  average  expectation  of  life  of  the  survivors  at  any 
age,  it  is  the  quotient  of  the  number  of  years  the  survivors  have  to 
live  in  succeeding  age  classes  divided  by  the  number  of  the  survivors. 

If,  therefore,  as  the  table  shows,  there  were,  14. 1  among  the  100,000 
who  survived  the  age  of  100,000  years,  and  for  which  we  could  as- 
sume by  direct  observation  or  estimate  that  each  of  these  would  live 

12.3+  25-2  =  37;5t  nr,-nn  the  average,  2.67  years;  then  from  the 
14.1  14-1 


234 


Annals  of  the  American  Academy. 


table  we  may  calculate  the  average  expectation  of  life  from  the  high- 
est age  to  the  youngest,  in  the  following  fashion  : 


Survivors  at  ioo  years  . 
Died  99-100  years  old  . 

Survivors  at  99  years    . 
Died  98-99  years  old   . 

Survivors  at  98  years    . 
Died  97-98  years  old   . 

Survivors  at  97  years    . 
Died  96-97  years  old   . 

Survivors  at  96  years   . 
etc. 


Num- 
ber of 
survi- 
vors. 

Years  of 

Survival 

of  the 
dying 
in  the 
year. 

of  the 
survi- 
vors 
of  the 
year. 

In  the 

higher 

age 
classes 

In  total 

14.I 

4.8 

1.8 
2-5 
8-3 
8.2 

14. 1 
18.9 
30.O 

46.6 

as  in 
col.  7 

37.5 
53-4 
74-8 

113-1 

as  in 
col.  6 

37-5 
53-4 
74.8 

113-1 

167.9 
col.  6 

18.9 
II. I 

30.0 
16.6 

46.6 
18.5 

65.I 
col.  7 

Aver- 
age 
dura- 
tion of 
life  in 
years. 


2.67 
2.86 

2.49 
2.4s 


2.58 

col.  8 


In  this  way  we  calculate  backward  the  average  expectation  of  life, 
or  the  average  duration  of  life,  of  each  age  down  to  the  first.  These 
numbers  express  the  order  of  mortality  for  each  age  up  to  the  highest. 
It  must  increase  with  every  fall  in  the  mortality  and  diminish  by  every 
increase  in  the  latter. 

If  we  seek  the  average  expectation  of  life  for  the  total  population, 
we  must  multiply  the  expectation  at  each  age  by  the  number  reaching 
that  age,  and  divide  the  sum  of  the  results  by  the  number  of  the  popu- 
lation. 

That  the  insight  into  the  expectation  of  life  is  very  important,  and 
that  a  comparison  of  it  for  different  countries  or  periods  may  lead  to 
valuable  results,  needs  no  demonstration.  On  the  other  hand,  that 
the  results  hold  good  only  for  a  population  of  a  given  place  and  at  a 
given  time — that  is,  for  an  aggregate  strictly  limited  in  time  and  space 
— lies  in  the  nature  of  the  problem. 

We  can,  indeed,  unite  the  deaths  and  living  population  for  several 
years  and  for  several  districts,  but  this  extension  of  the  field  for  which 
our  average  figures  are  obtained  does  not  change  the  essence  of  the 
aggregate  in  any  way.  The  coefficient  of  mortality  corresponds  to 
the  average  yearly  number  of  deaths  of  persons  of  a  given  age 
divided  by  the  average  number  of  living  persons  of  the  same  age. 

The  calculations  require  great  accuracy  and  a  clear  insight  into  the 


Theory  and  Technique  of  Statistics.  235 

problem.  They  are  mathematical  in  character,  or,  in  other  words, 
simply  analytical  consequences  from  given  elements.  The  greatest 
difficulty  lies  in  the  technical  statistical  processes  of  collecting  these 
elements. 

The  older  census  operations  called  only  for  the  age  of  persons,  and 
classed  them  in  a  few  broad  groups.  The  International  Statistical 
Congress  resolved,  in  1863,  that  in  enumerations  of  population  and  in 
the  classifications  of  death  the  year  of  birth  should  be  given.  This  has 
been  followed  partially.  For  complete  security  the  more  recent  enu- 
merations require  the  exact  date  of  birth. 

Greater  difficulty  is  found  in  the  double  ascertainment  of  the  age 
and  of  the  year  of  birth  for  the  persons  dying.  It  is  not  easy  to  obtain 
the  date  of  birth  and  death,  and  one  must  have  also  the  calculation  of 
the  age.  If  the  enumeration  is  taken  at  a  time  other  than  the  close 
of  the  year,  a  corresponding  division  must  be  made  for  the  births  and 
deaths.  The  complete  number  of  still-born,  with  distinction  of  sex 
and  time  of  birth,  as  in  the  case  of  the  population  at  large,  and  the 
deaths  cannot  properly  be  dispensed  with.  In  particular,  care  must 
be  taken  to  avoid  the  inaccuracies,  which,  unfortunately,  occur  so 
frequently  in  the  returns  of  age.  If  all  these  necessary  data  are 
unreliable,  or  if  some  of  them  are  missing,  the  result  must  be  open  to 
much  more  criticism,  since  probabilities  take  the  place  of  facts  in  the 
elements  of  calculation. 

The  most  frequent  of  these  assumptions  is  the  one  mentioned 
above,  that  of  the  deaths  of  persons  in  a  given  age,  one-half  belong 
to  each  of  the  possible  years  of  birth.  This  assumption  is  fairly  cor- 
rect for  the  higher  age  classes,  from  5  or  even  3  years  upward.  It  is 
inapplicable  to  childhood,  however,  since  the  number  of  those  who 
die  in  the  first  month  is  by  far  the  largest,  and  this  number  decreases 
noticeably  from  month  to  month  in  the  first  and  even  in  the  second 
year.  If,  therefore,  the  days  of  birth  and  death,  at  least  for  the  chil- 
dren, are  not  noted,  or  in  the  first  year  the  months  and  in  the  second 
the  quarters  distinguished,  then  nothing  remains  but  to  interpolate 
according  to  the  analogy  of  other  aggregates,  whereby  the  general 
consideration  of  the  conditions  of  the  particular  locality  should  not 
be  neglected. 

From  such  material  for  different  ages  only  a  limited  grouping  of 
ages  of  5-  or  10-year  periods  is  advisable.  If  the  figures  in  the  first 
instance  give  ages  only  by  such  periods,  the  interpolation  becomes  so 
difficult  that  the  results  cannot  be  regarded  with  confidence. 

Only  very  general  conclusions  can  be  drawn  from  the  calculation 
of  the  relation  of  all  deaths  to  the  living  population,  the  so-called 
death-rate.    As  Becker  has  shown,  this  general  rate  may  be  lower  in 


236     Annals  of  the  American  Academy. 

one  State  than  in  another,  which  in  all  age  classes  has  a  lower  mor- 
tality, in  case  the  latter  has  a  larger  number  of  children. 

None  the  less,  in  default  of  other  material,  such  estimates  as  Graunt 
and  Halley  applied,  even  to  calculating  the  population,  are  indis- 
pensable, and  must  be  regarded  as  proper  so  long  as  they  are  drawn 
from  sufficiently  analogous  conditions.  From  fragments  even  con- 
ditional approximations  can  be  gathered.  Here  may  be  mentioned 
the  investigation  of  population  in  earlier  centuries,  which  has  attracted 
much  attention  of  late.  (J.  Jastrow :  Die  Volkszahl  deutscher  Stadte 
zur  Ende  des  Mittelalters,  etc.  Ueberblick  uber  Stand  und  Mittel  der 
Forschung.     Berlin,  1886.) 

The  historical  development  of  the  calculation  of  mortality  tables  has 
been  presented  with  critical  acuteness  in  G.  F.  Knapp's  second  essay: 
"Zur  Theorie  des  Bevolkerungswechsels,  1874,  which  covers  the  field 
from  Graunt  to  Berg  (Befolkinags-Statistik,  N.  F.  II.  3,  i860);  Fair 
(English  Life  Table,  1864),  and  Becker.  At  about  the  same  time 
with  Becker's  "Theorie  der  Sterbetafeln,"  works  on  the  subject  ap- 
peared, in  1867,  as  follows  :  Wittstein:  Die  Mathematische  Statistik 
in  ihrer  Anwendung ;  Lazarus,  Ueber  Mortalitatsverhaltnisse,  and 
v.  Hermann :  Mortalitat  und  Vitalitat  in  Bayern,  Beitrage  z.  Stat. 
Bayerns,  Heft  XVII.  ;  further,  Knapp :  Ueber  die  Ermittelung  der 
Sterblichkeit,  1868,  and  Zeuner,  Abhandlungen  aus  der  mathema- 
tischen  Statistik,  1869.  In  1874  there  followed  another  group  of 
essays:  Knapp's  essay,  cited  above;  Becker:  Zur  Berechung  von 
Sterbetafeln,  Gutachtenfur  den  internationalen  Congress,  1874;  Lexis: 
Einleitung  in  die  Theorie  der  Bevolkerungsstatistik,  1875 ;  Bceckh's 
Sterblichkeitstafeln  fur  den  Preussischen  Staat,  1875,  use(i  above,  and 
Lewin  :  Denkschrift  fur  den  internationalen  statistischen  Congress  zur 
Pest.,  1876.  Essays  of  a  similar  character  have  been  published  by 
Armenante  and  Perozzo,  in  the  Annali  di  Statistica,  Vol.  I.,  1876; 
Ser.  2,  Vol.  12,  1880.  The  last  named,  with  a  preface  by  Lexis,  ap- 
peared in  translation  in  Conrad's  Jahrbuchern,  N.  F.,  1  Bd.  p.  162. 

Since  the  year  1876  R.  Boeckh  has  published,  on  the  basis  of  the 
material  collected  under  his  supervision  in  Berlin,  yearly  mortality 
tables,  which  are  unexcelled  in  the  character  of  the  material  and  the 
care  of  the  processes  (Veroffentlichungen  des  Statistischen  Bureaus 
der  Stadt  Berlin,  1878,  and  following  years).  These  tables  bring  all 
the  questions  of  the  equalization  of  ages,  of  the  still-born,  of  the  date 
of  enumeration,  of  influx  and  emigration,  and  the  union  with  previous 
years,  to  a  satisfactory  issue  in  the  clearest  and  most  unimpeachable 
manner. 

Other  works  of  importance  in  this  field  are : 

G.  Mayr :  Bewegung  der  Bevblkerung  in  Konigreich  Bayern,  Beilage 
zur  Stat.  v.  B.  Heft  XXXVIL,  1878. 


Theory  and  Technique  of  Statistics.  237 

v.  Berg:  Elements  demographiques  de  la  Suede,  1879. 

Harald  Westergaard :  Die  Lehre  von  der  Mortalitat  und  Morbilitat, 
1882. 

Frhr.  v.  Fircks:  Absterbeordnung,  Mortalitat,  Lebenserwartung,  und 
durchschnittliche  Lebensdauer  der  Preussischen  Bevolkerung,  Zeit- 
schrift  des  Preuss.  Stat.  Bur.,  1882,  p.  137. 

A.  J.  van  Pesch :  Table  de  mortality  pour  le  Pays  Bas,  calcule*e  sur 
les  donn6s  de  1 870-1880,  in  Bijdragen  van  het  Statistisch  Instituut,  No. 
3,  1885. 

W.  Fair:  Vital  Statistics,  edited  by  N.  A.  Humphreys,  1885. 

The  elements  for  international  comparison  for  the  years  1 865-1 883 
were  collected  by  Bodio  in  the  work,  Populatione,  Movimento  dello 
stato  civile,  1884. 

A  special  value  as  evidence  of  how  litde  statistical  probabilities  can 
be  generalized  beyond  the  field  of  observation  (g  1 1 1 ),  is  to  be  attached 
to  the  data  for  Iceland,  Greenland,  and  the  Faroe  islands,  as  given  by 
Westergaard,  to  the  Deutsche  Sterblichkeitstafeln  nach  den  Erfahr- 
ungen  von  23  Lebensversicherungs-Gesellschaften  im  Auftrage  des  Col- 
legiums  fur  Lebensversicherungs-wissenschaft  in  Berlin,  1883,  and  to 
the  observations  of  Jagor,  on  the  Mortality  of  Natives  and  Europeans 
in  East  India,  based  on  the  census  of  1 881  (Zeitschrift  fur  Ethnologie, 
Jahrgang  13.  Heft  II.  p.  92,  1886).      » 


INDEX  OF  NAMES. 


Achenwall.  9, 18  et  seq.,  36, 41, 49, 

75,  90,  103, 105 
Acherson,  41 
JEnea.s  Sylvius,  18 
Albrecht,  192 
Alphonso  I.,  18 
Arbuthnot,  34 
d'Argenson,  37,  40 
Aristotle,  22 
Armenante,  236 
Ascheton,  33 
Augustus,  16 
Avet,  69 
d'Avity,  Pierre,  21,  51 


B. 


Bachaumont,  23 

Baily,  52 

Balbi,  70,  72 

Ballois,  44 

Barral,  56 

Baumann,  36,  38 

Baumhauer,  61,  94 

de  Beaufort,  37,  41 

Becker,  K.,  94,  230,  235,  236 

Beckmann,  22 

Beguelin,  47 

Bender,  33 

v.  Berg,  79,  237 

Bernouilli,  33,  144 

Besold,  Chr.,  26 

Block,  M.,  23,  93,  98 

Bodemann,  26 

Bodin,  Jean,  25 

Bodio,  69,  86,  237 

Boeckh,  A.,  16 

Boeckh,  R.,  27,  28, 47, 95, 233,  236 


Boeder,  26 

Boeking,  17 

Boetticher,  41 

Borromeo,  20 

Bose,  22 

Botero,  Giov.,  20,  21 

Boulainvilliers,  27 

Brachelli,  166 

Brandis,  49 

Bremiker,  192 

le  Bret,  38 

Brune,  53 

v.  Brunn,  49 

Buchsenschiitz,  16 

Buckle,  85,  88 

Busching,  9,  24  et  seq.,  28,  49,  51 


C. 

Cambaceres,  44 

Caporale,  98 

Carmer,  Count,  38 

Casper,  72 

Chabral,  Count,  55 

Chaptal,  43 

Charles  Emanuel,  20 

Charles  of  Calabria,  18 

Clinton,  16 

Colbert,  27 

Condorcet,  39,  72,  149,  182 

Coming,  Herm.,  21,  22  et  seq. 

Constantin  Porphyrogeneta,  17 

Contarini,  21 

Corradi,  86 

Correnti,  C,  69 

Cournot,  77,  95 

Crelles,  192 

Crome,  40,  41 

v.  Czornig,  63 

(239) 


240         Theory  and  Technique  of  Statistics. 


Deferriere,  44 
Derham,  34 
Deslandes,  39 
Desparcieux,  39 
Dieterici,  57 
Dohm,  38 
Donnant,  44,  49 
Drobisch,  87 
Droz,  50 

Duchatel-Neuville,  73 
Dumas,  Al.,  73 
Duncker,  M.,  16 
Dupin,  78 
Duquesnoy,  43 


Edward  III.,  18 
Ehrmann,  41 
Eichhorn,  51 
Elzevir,  21 
Engel,  94,  172,  1 85 
Engelhardt,  48 
Euler,  39 


Fabn,  37 

Fabricius,  94 

Fallati,  77 

Fair,  4,  78,  236,  237 

Ferber,  57 

Fichte,  51 

Ficker,  63 

Fidicin,  18 

Finlaison,  53,  64 

v.  Fircks,  237 

Firmian,  38 

Fletcher,  78 

Format,  33 

Fourier,  73 

de  Fourier,  44,  72 

Francis  I.,  29 

Franscini,  68 

Frantz,  A.,  93 

Franzl,  53 

Frederick  II.,  Emperor,  18 

Frederick  II.,  of  Prussia,  9,  27, 

Frederick  William  I.,  27 

Flicker,  63 

Froumenteau,  N.,  26 


46 


G. 

Gaillard,  91 

Galanti,  18,  38 

Garve,  50 

Gaspari,  41 

Gatterer,  36,  51 

Gauss,  39 

de  Gerando,  73 

Gioja,  45,  76,  143 

Gneist,  17 

Godefroy,  73 

Goebel,  21 

Gollmert,  18 

Graetzer,  30,  224 

Graunt,  John,  30,  32,  34,  236 

Grisi,  69 

Guerry  de  Champneuf,  55,  74 


H. 


Haller,  51 

Halley,  Edm.,  9,  30  et  seq.,  221  et 

seq.,  236 
Hassel,  45,  49 
Haushofer,  96,  21 1 
Haussner,  134 
Heeren,  49,  53 
Heffter,  51 
Hegel,  51 
Heiberg,  73 
Henri  IV.,  26 
Henry  VIII.,  29 
Herbin,  43 
Hermann,  C.  F.,  16 
v.  Hermann,  58,  73,  92,  230,  236 
Herodotus,  15,  16 
Herschel,  85',  97 
v.  Hertzberg,  36,  38 
Herz,  22 
Heuermann,  87 
Heuschling,  79 
Hildebrand,  17,  59,  93,  233 
Hobbes,  30 
v.  Hoeck,  41 
Hoffmann,  47,  57,  71 
v.  Holtzendorff,  61 
v.  Holzgethan,  53 
Hufeland,  50 
v.  Humboldt,  112 
Huygens,  33 
Hygin,  17 


Index  of  Names. 


241 


I. 

Iginio,  91 

v.  Inama-Sternegg,  66,  93 

d'lvernois,  74 

J. 

Jacob,  J.,  50 
Jagor,  237 
Janotti,  21 
Jastrow,  236 
John  V.,  22,  30,  49 
Jonak,  91 
Jurgen-Hanssen,  73 


Kaestner,  39 

Kant,  51 

Kennedy,  78 

Kerseboom,  34 

King,  31,  34 

Kliiber,  51 

Knapp,  30,  33,  34,  39,  72,  88,  94, 

221,  224,  236 
Knies,  77 
Kolb,  166 
Kotschubey,  67 
Kraus,  50 

Krug,  Leopold,  46-47,  48 
Kriiger,  16 
v.  Kubeck,  62 


Lachmann,  17 
Lacroix,  52 
de  Laet,  Jean,  21 
Lafarge,  52 
Landau,  G.,  59 
Laplace,  52,  72 
Lappenberg,  18 
Larruga,  38 
Lavoisier,  42 
Lazarus,  236 
Legoyt,  166 
v.  Leibnitz,  26,  31 
Leopoldo  II.,  38 
Lewin,  236 
Lexis,  93,  95, 136,  236 
Lichtenstern,  49 


Littrow,  52 
Lottini,  25 
Louis  XIV.,  27 
Louvois,  27 
Luca,  37,  93 
Lucam,  62 
Liider,  37,  49,  53 
v.  Luttwitz,  73 
Lycurgus,  16 

M. 

MacCulloch,  50 

Machiavelli,  18 

Madoz,  70 

Maestro,  69 

v.  Malchus,  72 

dela  Malle,  17 

Malthus,  40,  50,  73 

al-Mamum,  17 

Mannert,  37,  53 

Marey,  97,  136,  196 

Martin,  166 

Mauvillon,  40 

Mayr,  93,  97,  196,  236 

Meitzen,  3,  4  et  seq.,  6i,  92 

Memminger,  58 

Menander,  38 

Messance,  39 

Messedaglia,  86 

v.  Metzburg,  62 

Meusel,  36,  53 

Mill,  J.  S.,  98 

Milne,  52 

Minano,  70 

Mirabeau,  40 

Moheau,  40 

v.  Mohl,  R.,  91 

de  Moivre,  34 

Molossi,  69 

Mommsen,  Th.,  17 

Mone,  76 

Montalivet,  45 

de  Montbret,  43 

Mont  Palau,  A.,  37 

Monty  on,  40 

Moreau  de  Jonn£s,  16,  55,  77,  92 

Morgan,  39,  53 

Morpurgo,  86 

Moser,  Justus,  51 

Moser,  Lud.,  73 

Mulhall,  166 

Miinster,  Seb.,  20,  24,  51 


242 


Theory  and  Technique  of  Statistics. 


N. 
Napoleon,  44 
Nardi,  91 
Necker,  38,  43 
Nessmann,  186 
de  Neufchateau,  43 
Neumann,  Casper,  30,  31, 221,  224 
Newsholme,  4 
Niebuhr,  17 
Niemann,  49,  53 
Nieuwentyt,  34 
Noack,  40 


Obrecht,  G.,  25 
Ockhart,  41 
v.  Oettingen,  87 
Oldenburger,  21,  22  et  seq. 
Otto,  Everard,  22 


P. 
Padovani,  71 
Pascal,  33 
Pasquier,  26 
Pelgrave,  18 
Peter  the  Great,  67 
Petigny,  55 
Petitot,  26 

Petty,  Wm.,  30,  34,  209 
Perozzo,  97,  197,  236 
van  Pesch,  237 
Peuchet,  43,  44 
Pfister,  59 
Philip  II.,  26 
Philippi,  17 
Piccolomini,  18 
Plaifair,  41 
de  Plaza,  70 
Poepping,  21 
Pogodin,  67 
Poiitz    50 

de  la  Pommelles,  40 
Porter,  78 
Potlock,  76,  95 
Price,  39 
Prudhomme,  44 
Putter,  51 

Q- 

Quadri, 18 

Quetelet,  10,  62,  73-74,  78,  85,  149 


R. 

Racioppi,  93 

Raglowich,  45 

Rameri,  93 

Rameses.  15 

Ran  del,  41 

v.  Ranke,  L.,  26 

Ratzel,  92 

Rau,  50 

v.  Raumer,  18 

Raynal,  40 

v.  Reden,  72,  77 

Rehberg,  49 

Rehnisch,  29,  224 

Rein  hard,  36 

Remer,  41 

Ricardo,  50 

Richard  II.,  18 

Richter,  A.  L.,  29 

v.  Richthofen,  Ferd.,  15 

Riciotti,  35 

Rickmann,  64 

Riehl,  92 

Ritter,  C,  51 

Romagnosi,  76 

Roncaglia,  69 

Roscher,  W.,  25,  92 

v.  Rotteck,  50 

Rudorff,  17 

Rumelin,  88,  95,  98,  21 1 


S. 

Sagittarius,  22 
Salmon,  Thomas,  22 
Sansovino,  Fr.,  20 
Sartorius,  50 
Say,  50,  209,  210 
v.  Scheel,  209,  215 
v.  Schlieben,  53,  58 
Schlomilch,  192 
Schlosser,  51 
v.  Schlozer,  36,  49,  53,  91 
Schmeitzel,  22,  23 
v.  Schmettau,  28 
v.  Schmidtberg,  49 
Schmidt,  73 
Schm  oiler,  61,  88 
Schnabel,  53 
Schon  emann,  40 
Schubart,  22 
Schubert,  72,  77 


Index  of  Names. 


243 


v.  Seckendorf,  26 
Seitwein,  40 
Senior,  73 
Servius  Tullius,  16 
Sigwart,  89,  98, 153,  211 
Simler,  Josias,  21 
Simpson,  39 
Sinapius,  40 
Sinclair,  23 
Sismondi,  50 
v.  Sittewald,  23 
Smith,  Adam,  50 
Smith,  R.  M.,  4,  5 
Smits,  61 
Solon,  16 

Sprengel,  28,  36  et  seq 
v.  Stein,  46 
v.  Stein,  Lorenz,  91 
Stenzel,  18 
Stewart,  50 
Storch,  6y 
v.  Struensee,  40 
Struyk,  Nic,  34 
Sue,  Eugene,  73 
Sully,  26 
vSiissmilch,  9,  io,  29  et  seq.,  38, 
49.  53.  72, 103 


T. 


Tammeo,  97 
Tetens,  39 
Thiers,  55 
Thomas,  192 
Thomasius,  22 
de  Thou,  21 
Thurmann,  23 
Tobler,  17 
de  Tolosan,  40 


Tonti,  Lorenzo,  33 
de  la  Tour,  23 


v.  Vega,  192 
v.  Viebahn,  92 
Villeneuve-Bargemont,  73 
Villerme,  72 
Villot,  55 
Vischer,  78 

W. 

Wagner,  86,  87,  96 
Waldemar  II.,  18 
Wappaus,  91-92 
Wargentin,  39,  230 
Welker,  51 
Westergaard,  237 
William  the  Conqueror,  17 
Williamson,  J.,  31 
Wirth,   M.,  92 
Wittstein,  94,  192,  236 
de  Witt,  Jean,  33 
Wolff,  Chr.,  34 

Y. 

Young,  Arthur,  40 

Z. 

Zachariae,  51 
Zambetti,  91 
Zermelo,  37 
Zeune,  51 
Zeuner,  94 
Zimmermann,  E.,  37 
Zuccagni-Orlandini,  69,  91 


The  American  Academy 

OB1 

Political  and  Social  Science 


PHILADELPHIA 


President, 
EDMUND  J.  JAMES,  Ph.D.,  University  of  Pennsylvania. 


HENRY  C.  LEA, 
2000  Walnut  Street. 


Vice-Presiden  is , 
Prof.  F.  H.  GIDDINGS,  A.  M. 
Bryn  Mawr  College. 


Secretaries. 


Corresponding  Sec'y, 

R.  P.  FALKNER,  Ph.D., 

Germantown,  Phila. 


Treasurer, 

STUART  WOOD, 

400  Chestnut  Street. 


Prof.  W.  P.  HOLCOMB,  Ph.D., 
Swarthmore  College. 

General  Secy, 
C.  R.  WOODRUFF, 
1200  Chestnut  Street. 

Librarian, 

JOHN  L.  STEWART, 

Manual  Training  School. 


GENERAL  ADVISORY  COMMITTEE 


DR.  C.  K.  ADAMS, 

President  of  Wisconsin  University. 

DR.  E.  B.  ANDREWS, 

President  of  Brown  University. 

DR.  JAMES  B.  ANGELL, 

President  of  Michigan  University. 

PROF.  C.  F.  BASTABLR, 

Dublin  University. 
PROF.  F.  W.  BLACKMAR, 

University  of  Kansas. 
J.  G.  BOURINOT,  C.M.G.,  PH.D.,  D.C.I,., 

Ottawa,  Canada. 
PROF.  J.  W.  BURGESS, 

Columbia  College. 
HON.  THOMAS  M.  COOLEY, 

Ann  Arbor,  Mich. 
PROF.  R.  T.  ELY, 

Wisconsin  University. 
PROF.  HENRY  W.  FARNAM, 

Yale  University. 
PROF.  W.  W.  FOLWELL, 

University  of  Minnesota. 

HON.  LYMAN  J.  GAGE, 

Chicago,  HI. 
PROF.  JOHN  K.  INGRAM,  LL.D., 

Trinity  College,  Dublin. 
PROF.  J.  W.  JENKS, 

Cornell  University. 


DR.  WM.  PRESTON  JOHNSTON, 

President  of  Tulane  University. 
RIGHT  REV.  JOHN  J.  KEANE,  D.  D., 

Catholic  University  of  America. 
PROF.  BERNARD  MOSES, 

University  of  California. 
PROF.  J.  S.  NICHOLSON,  M.  A., 

Edinburgh  University. 
PROF.  F.  G.  PEA  BODY, 

Harvard  College. 
PROF.  HENRY  SIDGWICK, 

Cambridge  University. 
PROF.  WILLIAM  SMART, 

Queen  Margaret  Col.,  Glasgow. 
SIMON  STERNE,  Esq., 

New  York  City. 
HANNIS  TAYLOR,  Esq., 

Mobile,  Ala. 
PROF.  J.  B.  THAYER, 

Harvard  Law  School. 
PROF.  F.  N.  THORPE, 

University  of  Pennsylvania. 
DR.  FRANCIS  A.  WALKER, 

Pres.  Mass.  Inst,  of  Technology- 
PROF.  WOODROW  WILSON, 

Princeton  University. 
LESTER  F.  WARD,  Esq., 

Washington,  D.  C. 


THE  AMERICAN  ACADEMY  OF  POLITICAL  AND 

SOCIAL   SCIENCE. 

The  American  Academy  of  Political  and  Social  Science 
was  formed  in  Philadelphia,  December  14,  1889,  for  the 
purpose  of  promoting  the  Political  and  Social  Sciences. 

While  it  does  not  exclude  any  portion  of  the  field  indi- 
cated in  its  title,  yet  its  chief  object  is  the  development  of 
those  aspects  of  the  Political  and  Social  Sciences  which 
are  either  entirely  omitted  from  the  programmes  of  other 
societies,  or  which  do  not  at  present  receive  the  attention 
they  deserve. 

Among  such  subjects  may  be  mentioned:  Sociology, 
Comparative  Constitutional  and  Administrative  Law,  Phi- 
losophy of  the  State,  and  such  portions  of  the  field  of  Poli- 
tics, including  Finance  and  Banking,  as  are  not  adequately 
cultivated  by  existing  organizations. 

A  special  effort  will  be  made  to  collect  and  publish  mate- 
rial which  will  be  of  use  to  students,  and  which  does  not 
now  reach  the  public  in  any  systematic  way,  as,  for  ex- 
ample, the  texts  in  English  of  the  Constitutions  of  leading 
foreign  countries;  regular  accounts  of  current  instruction 
in  Political  and  Social  topics  at  home  and  abroad  ;  descrip- 
tive bibliographies  ;  discussions  of  Municipal  Government,  etc. 

It  will  be  seen  that  the  Academy  will  supplement  the 
efforts  of  existing  societies  of  similar  aims,  and  will  sub- 
stantially strengthen  their  work  by  contributing  its  share 
to  beget  a  deeper  and  more  widespread  interest  in  the  gene- 
ral subject  of  Political  and  Social  Science. 

The  plan  of  the  Academy  includes  regular  scientific  meet- 
ings for  the  presentation  of  papers  and  communications, 
establishment  of  a  library,  and  the  dissemination  of  knowl- 
edge on  Political  and  Social  topics  through  its  publications 
and  by  such  other  means  as  may  seem  suitable. 

During  the  winter,  regular  monthly  meetings  have  been 
held  since  the  Academy  was  formed  at  which  the  papers 
submitted  have  been  read  and  discussed. 


To  carry  on  the  work  of  the  Academy  satisfactorily,  large 
funds  are  necessary.  The  income  of  the  Academy  at  present 
is  derived  from  the  Annual  Membership  Fee,  which  is  $5.00 ; 
the  Life  Membership  Fee,  which  is  $100 ;  and  from  the  contri- 
butions of  those  who  may  be  willing  to  assist  in  its  work.  It 
is  desired  to  secure  the  establishment  of  prizes  and  fellowships. 

Anyone  may  become  a  member  on  being  approved  by 
the  Council  and  paying  the  Annual  or  Life  Membership  Fee. 
Members  are  entitled  to  receive  the  regular  publications  of 
the  Academy,  submit  papers  and  communications,  and  to 
attend  and  take  part  in  all  scientific  meetings.  Life  mem- 
bers are  exempt  from  all  annual  fees. 

The  list  of  members  now  includes  the  names  of  nearly  all 
the  prominent  thinkers  and  writers  on  Political,  Economic 
and  Social  topics  in  the  United  States  and  Canada,  and  many 
in  Europe. 

The  co-operation  of  all  persons  interested  in  the  scientific  in- 
vestigation of  Political  and  Social  affairs  is  earnestly  solicited. 

The  proceedings  of  the  Academy  are  published  in  the 
form  of  a  periodical  called  the  Annals  of  the  American 
Academy  of  Political  and  Social  Science,  which, 
together  with  such  other  matter  as  may  be  published  for 
that  purpose,  is  sent  to  all  members  of  the  Academy  free 
of  charge.  A  copy  of  the  current  number  of  the  Annals 
will  be  sent  to  anyone  for  examination. 

Papers  and  communications  which  the  writers  wish  to 
submit  to  the  Academy  with  a  view  to  their  being  read  in  a 
Scientific  Session  and  subsequently  published  in  the  Proceed- 
ings, as  well  as  applications  for  membership,  should  be  sent 
to  the  following  address : 

American  Academy  of  Political  and  Social  Science, 

STATION  B,  PHILADELPHIA,  PA. 

N.  B. — Fees  and  contributions  may  be  remitted  by  postal 
order  on  Philadelphia,  or  by  draft  en  New  York,  drawn  to 
the  order  of  the  Treasurer,  Mr.  Stuart  Wood,  400  Chestnut 
Street,  Philadelphia 


Publications  of  the  Academy,  (1890-91.) 

Among  the  papers  which  were  submitted  to  the  Academy  and  sent 
to  its  members  in  the  form  of  the  First  Volume  of  the  Annaes,  were 
the  following : 
Origin  of  Connecticut  Towns,  Prof.  C.  M.  Andrews,  Bryn  Mawr 

College. 
Character  of  Villein  Tenure,   Prof.   W.  J.   Asheey,  University  of 

Toronto. 
Historical  vs  Deductive  Political  Economy,  Prof.  E.  von  Boehm- 

Bawfrk,  Ministry  of  Finance,  Vienna,  Austria. 
The  Austrian  Economists,  Prof.  E.  von  Boehm-Bawerk. 
Canada  and  the  United  States,   Hon.  J.   G.  Bourinot,   C.   M.   G., 

Ottawa,  Canada. 
Law  of  Wages  and  Interest,  Prof.  J.  B.  Ci<ark,  Smith  College. 
Academic  Instruction  in  Political  and  Economic  Science  in  Italy, 

Prof.  R.  P.  Faekner. 
International  Criminal  Law  Association,  Prof.  R.  P.  Faekner. 
Province  of  Sociology,  Prof.  Frankein  H.  Giddings,  Bryn  Mawr 

College. 
German  Economic  Association,  Mr.  John  H.  Gray,  Berlin. 
Compulsory  Voting,  Frederick  Wm.  Hoees,  Esq.,  New  York  City. 
Genesis  of  a  Written  Constitution,  Prof.  Wm.  C.  Morey,  University 

of  Rochester. 
Decay    of    State    and    Local    Government,    Prof.    S.    N.    Patten, 

University  of  Pennsylvania. 
"  Original  Package  "  Case,  Prof.  C.  Stuart  Patterson,  Law  School, 

University  of  Pennsylvania. 
On  the  Conception  of   Sovereignty,    Prof.  D.  G.  Ritchie,  Jesus 

College,  Oxford,  England. 
Original   Features   of   the   United   States    Constitution,    Dr.  James 

Harvey  Robinson. 
Philadelphia  Social  Science  Association,  Jos.  G-  Rosengarten,  Esq., 

Philadelphia. 
Instruction  in  Public  Law  and  Economics  in  German  Universities, 

Leo  S.  Rowe,  Berlin. 
Law  of  Nature,  Prof.  F.  M.  Taylor,   Albion  College. 
Wealth  Concept,  Prof.  Chas.  A.  TuTTEE,  Amherst  College. 
Railroad  Passenger  Fares  in  Hungary,  Jane  J.  WETHEREEE. 
Railroad  Passenger  Tariffs  in  Austria,  Jane  J.  WETHEREEE. 
Critique  of  Wages  Theories,  Stuart  Wood,  Ph.  D.. 

Besides  the  four  numbers  of  the  First  Volume,   there  were  four 
Supplements,  as  follows : 
Public  Health  and  Municipal  Government.     By  Dr.  John  S.  Bieeings, 

U.  S.  A.  Supplement,  February,  iSgi. 

History,  Theory,  and  Technique  of   Statistics.     By  Prof.  August 
MeiTzen  ;  translated  by  Roeand  P.  Falkner,  Ph.  D.     Part  I. 

Supplement,  March,  i8gi. 
Handbook  of  the  American  Academy  of  Political  and  Social  Science. 

Supplement,  April,  1891. 
History,  Theory,  and  Technique  of   Statistics.      By  Prof.  August 
Meitzen  j  translated  by  Roeand  P.  Faekner,  Ph.  D.     Part  II. 

Supplement,  May,  1891. 


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